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. 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.
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.
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
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. 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.
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.
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
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!
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.