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Permutations and Combinations

In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged so that the vowels always come together?

Mathematics Mcqs, Permutations and Combinations /
In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged so that the vowels always come together?

A. 10080
B. 4989600
C. 120960
D. None of these

In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged so that the vowels always come together? Read More »

Mathematics Mcqs, Permutations and Combinations

How many 4-letter words with or without meaning, can be formed out of the letters of the word, ‘LOGARITHMS’, if repetition of letters is not allowed?

Mathematics Mcqs, Permutations and Combinations /
How many 4-letter words with or without meaning, can be formed out of the letters of the word, ‘LOGARITHMS’, if repetition of letters is not allowed?

A. 40
B. 400
C. 5040
D. 2520

How many 4-letter words with or without meaning, can be formed out of the letters of the word, ‘LOGARITHMS’, if repetition of letters is not allowed? Read More »

Mathematics Mcqs, Permutations and Combinations

In how many different ways can four books A, B, C and D be arranged one above another in a vertical order such that the books A and B are never in continuous position?

Mathematics Mcqs, Permutations and Combinations /
In how many different ways can four books A, B, C and D be arranged one above another in a vertical order such that the books A and B are never in continuous position?

A. 9
B. 12
C. 14
D. 18
Explanation:
The number of arrangement in which A and B are not together
= Total number of arrangements
= Number of arrangements in which A and B are together =4!-3!x2! = 24-12 =12.

In how many different ways can four books A, B, C and D be arranged one above another in a vertical order such that the books A and B are never in continuous position? Read More »

Mathematics Mcqs, Permutations and Combinations

There are two identical red, two identical black, and two identical white balls.In how many different ways can the balls be placed in the cells (Each cell to contain one ball) shown above such that balls of the same colour do not occupy any two consecutive cells?

Mathematics Mcqs, Permutations and Combinations /
There are two identical red, two identical black, and two identical white balls.In how many different ways can the balls be placed in the cells (Each cell to contain one ball) shown above such that balls of the same colour do not occupy any two consecutive cells?

A. 15
B. 18
C. 24
D. 30

Explanation:
Case I : 2 balls of the same colour and two balls are a different colour are arranged.
Two balls of the same colour and two balls of different colours can be arranged together in which two balls of the same colour are adjacent =4!/2!x2! = 6 ways
Therefore, Total number of arrangements = 6×3 =18 ways
Case II : Two colours out of 3 can be selected in = 3C1 = 3ways
Now 2 balls of each colour can be arranged alternatively in 2 ways
Thus 4 balls can be arranged(two of each colours)
= 3×2 = 6ways
Hence total number of arrangements = 18+6 =24 ways

There are two identical red, two identical black, and two identical white balls.In how many different ways can the balls be placed in the cells (Each cell to contain one ball) shown above such that balls of the same colour do not occupy any two consecutive cells? Read More »

Mathematics Mcqs, Permutations and Combinations

Twelve people from a club, by picking lots. One of them will host a dinner for all once in a month. The number of dinners a particular member has to host in one year is________?

Mathematics Mcqs, Permutations and Combinations /
Twelve people from a club, by picking lots. One of them will host a dinner for all once in a month. The number of dinners a particular member has to host in one year is________?

A. One
B. Zero
C. Three
D. Cannot be determined
Explanation:
We cannot predicted the number of dinners that the particular number has to host in one year.

Twelve people from a club, by picking lots. One of them will host a dinner for all once in a month. The number of dinners a particular member has to host in one year is________? Read More »

Mathematics Mcqs, Permutations and Combinations

A person ordered 5 pairs of black socks and some pairs of brown socks. The price of a black pair was thrice that of a brown pair while preparing the bill the bill clerk inter-changed the number of black and brown pairs by mistake which increased the bill by 100% what was the number of pair of brown socks in the original order?

Mathematics Mcqs, Permutations and Combinations /
A person ordered 5 pairs of black socks and some pairs of brown socks. The price of a black pair was thrice that of a brown pair while preparing the bill the bill clerk inter-changed the number of black and brown pairs by mistake which increased the bill by 100% what was the number of pair of brown socks in the original order?

A. 10
B. 15
C. 20
D. 25
Explanation:
Let the bought x pairs of brown socks and the price of each brown pair be Y.
Then total cost = 5x3Y+xy
Changed cost = 5xY+x*3Y
According to the question .
5y+3xy –(15y+xy)/15y+xy x 100% = 100%
=> 5y+3xy-15y-xy/ 15y+xy x100% = 100%
=> 5y+3xy = 15y+xy+15y+xy
=> 5y+3xy = 30y+2xy
=> xy= 25y
=> x=25.
Hence the original pair of brown socks = 25.

A person ordered 5 pairs of black socks and some pairs of brown socks. The price of a black pair was thrice that of a brown pair while preparing the bill the bill clerk inter-changed the number of black and brown pairs by mistake which increased the bill by 100% what was the number of pair of brown socks in the original order? Read More »

Mathematics Mcqs, Permutations and Combinations

A two number committee comprising of one male and the female number is to be constituted out of five male and 3 females. Amongst the females, Ms. A refused to be number committee in which Mr.B is taken as the number of how many different ways can the committee be constituted?

Mathematics Mcqs, Permutations and Combinations /
A two number committee comprising of one male and the female number is to be constituted out of five male and 3 females. Amongst the females, Ms. A refused to be number committee in which Mr.B is taken as the number of how many different ways can the committee be constituted?

A. 11
B. 30
C. 14
D. 20
Explanation:
For each visualization let us name the females and Females(3) Males(5)
A B C D E F G H
Since A cannot go with B.
She will make team with four males in four ways AD,AF,AG,AH.
Since there is no compulsion with females C and E.
They can make team with 5 males in 5 different ways each.
Therefore, Total number of ways = 4+5+5 =14

A two number committee comprising of one male and the female number is to be constituted out of five male and 3 females. Amongst the females, Ms. A refused to be number committee in which Mr.B is taken as the number of how many different ways can the committee be constituted? Read More »

Mathematics Mcqs, Permutations and Combinations

A selection is to be made for one post of principal and two posts of vice-principal amongst the six candidates called for the interview only two are eligible for the post of principal while they all are eligible for the post of vice-principal. The number of possible combinations of selectees is___________?

Mathematics Mcqs, Permutations and Combinations /
A selection is to be made for one post of principal and two posts of vice-principal amongst the six candidates called for the interview only two are eligible for the post of principal while they all are eligible for the post of vice-principal. The number of possible combinations of selectees is___________?

A. 4
B. 12
C. 18
D. None of these
Explanation:
Total number of ways = 2C1 . 5C2 = 2 x 5!/3!2! = 2 x 10 = 210

A selection is to be made for one post of principal and two posts of vice-principal amongst the six candidates called for the interview only two are eligible for the post of principal while they all are eligible for the post of vice-principal. The number of possible combinations of selectees is___________? Read More »

Mathematics Mcqs, Permutations and Combinations

A student has to opt for 2 subjects out of 5 subjects for a course. Namely commerce, economics, statistics, mathematics 1 and Mathematics 2, Mathematics 2 can be offered only if mathematics 1 has also opted. The number of different combinations of two subjects which can be opted is_________?

Mathematics Mcqs, Permutations and Combinations /
A student has to opt for 2 subjects out of 5 subjects for a course. Namely commerce, economics, statistics, mathematics 1 and Mathematics 2, Mathematics 2 can be offered only if mathematics 1 has also opted. The number of different combinations of two subjects which can be opted is_________?

A. 5
B. 6
C. 7
D. 18

Explanation:
Number of ways of opting a subject other than Mathematics II = 4C2. = 4x3x2!/2!x2 = 6.
Number of ways of selection of Mathematics II = 1
Therefore, Total Number of ways = 6+1 =7.

A student has to opt for 2 subjects out of 5 subjects for a course. Namely commerce, economics, statistics, mathematics 1 and Mathematics 2, Mathematics 2 can be offered only if mathematics 1 has also opted. The number of different combinations of two subjects which can be opted is_________? Read More »

Mathematics Mcqs, Permutations and Combinations