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Mathematics Mcqs

A bag contains nine yellow balls, three white balls and four red balls. In how many ways can two balls be drawn from the bag?

A bag contains nine yellow balls, three white balls and four red balls. In how many ways can two balls be drawn from the bag?

A. ⁹C₂
B. ³C₂
C. ¹⁶C₂
D. ¹²C₂
Explanation:
Total number of balls = 9 + 3 + 4
Two balls can be drawn from 16 balls in ¹⁶C₂ ways.

A bag contains nine yellow balls, three white balls and four red balls. In how many ways can two balls be drawn from the bag? Read More »

Mathematics Mcqs, Permutations and Combinations

How many four digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9}

How many four digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9}

A. 60
B. 360
C. 120
D. 240
Explanation:
The given digits are 1, 2, 3, 5, 7, 9
A number is even when its units digit is even. Of the given digits, two is the only even digit.
Units place is filled with only ‘2’ and the remaining three places can be filled in ⁵P₃ ways.
Number of even numbers = ⁵P₃ = 60.

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Mathematics Mcqs, Permutations and Combinations

How many four digit numbers can be formed using the digits {1, 3, 4, 5, 7,9}(repetition of digits is not allowed)?

How many four digit numbers can be formed using the digits {1, 3, 4, 5, 7,9}(repetition of digits is not allowed)?

A. 360
B. 60
C. 300
D. 180
Explanation:
The given digits are six.
The number of four digit numbers that can be formed using six digits is ⁶P₄ = 6 * 5 * 4 * 3 = 360.

How many four digit numbers can be formed using the digits {1, 3, 4, 5, 7,9}(repetition of digits is not allowed)? Read More »

Mathematics Mcqs, Permutations and Combinations

The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is_________?

The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is_________?

A. (6!)2
B. 6! * ⁷P₆
C. 2(6!)
D. 6! * 7
Explanation:
We can initially arrange the six boys in 6! ways.
Having done this, now three are seven places and six girls to be arranged. This can be done in ⁷P₆ ways.
Hence required number of ways = 6! * ⁷P₆

The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is_________? Read More »

Mathematics Mcqs, Permutations and Combinations

A letter lock consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most__________?

A letter lock consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most__________?

A. 216
B. 243
C. 215
D. 729
Explanation:
Since each ring consists of six different letters, the total number of attempts possible with the three rings is = 6 * 6 * 6 = 216. Of these attempts, one of them is a successful attempt.
Maximum number of unsuccessful attempts = 216 – 1 = 215.

A letter lock consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most__________? Read More »

Mathematics Mcqs, Permutations and Combinations

A committee has 5 men and 6 women. What are the number of ways of selecting a group of eight persons?

A committee has 5 men and 6 women. What are the number of ways of selecting a group of eight persons?

A. 165
B. 185
C. 205
D. 225
Explanation:
Total number of persons in the committee = 5 + 6 = 11
Number of ways of selecting group of eight persons = ¹¹C₈ = ¹¹C₃ = (11 * 10 * 9)/(3 * 2) = 165 ways.

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Mathematics Mcqs, Permutations and Combinations

What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected?

What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected?

A. 100
B. 60
C. 30
D. 20
Explanation:
The number of ways to select three men and two women such that one man and one woman are always selected = Number of ways selecting two men and one woman from men and five women
= ⁴C₂ * ⁵C₁ = (4 * 3)/(2 * 1) * 5
= 30 ways.

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Mathematics Mcqs, Permutations and Combinations

A committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?

A committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?

A. 150
B. 200
C. 250
D. 300
Explanation:
The number of ways to select two men and three women = ⁵C₂ * ⁶C₃
= (5 *4 )/(2 * 1) * (6 * 5 * 4)/(3 * 2)
= 200

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Mathematics Mcqs, Permutations and Combinations

The number of permutations of the letters of the word ‘MESMERISE’ is___________?

The number of permutations of the letters of the word ‘MESMERISE’ is___________?

A. 9!/(2!)2 3!
B. 9!/(2!)3 3!
C. 9!/(2!)2 (3!)2
D. 5!/(2!)2 3!
Explanation:
n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways.
The letter pattern ‘MESMERISE’ consists of 10 letters of which there are 2M’s, 3E’s, 2S’s and 1I and 1R.
Number of arrangements = 9!/(2!)2 3!

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Mathematics Mcqs, Permutations and Combinations

The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places?

The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places?

A. 720
B. 144
C. 120
D. 36
Explanation:
The word MEADOWS has 7 letters of which 3 are vowels.
-V-V-V-
As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways.
Hence the total ways are 24 * 6 = 144.

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Mathematics Mcqs, Permutations and Combinations