permutations and combination mcq Model Questions & Answers, Practice Test for ibps rrb so officer sclae 2 3 single exam 2024
ibps rrb so officer sclae 2 3 single exam 2024 SYLLABUS WISE SUBJECTS MCQs
Number System
Lcm & Hcf
Ratio & Proportion
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Permutations & Combination
How many new words are possible from the letters of the word PERMUTATION?
Answer: (b)
Number of 11 letter words formed from the letter
P, E, R, M, U, T, A, I, O, N = 11!/2!.
Number of new words formed
= total words – 1 = 11!/2! – 1.
From 6 boys and 7 girls a committee of 5 is to be formed so as to include atleast one girl. The number of ways this can be done is
Answer: (d)
From total 13 members 5 can be select as $^13C_5$
For at least one girl in the committee, number of ways are $^13C_5 – ^6C_1$
From a group of 6 men and 4 women a committee of 4 persons is to be formed. In how many different ways can it be done so that the committee has at least one woman?
Answer: (a)
Reqd. no. of ways
= $4C_1 × 6C_3 × 4C_2 × 6C_2 × 4C_3 × 6C_1 + 4C_4$
= 4 × ${6 × 5 × 4}/{1 × 2 × 3} + {4 × 3}/{1 × 2} × {6 × 5}/{1 × 2} + {4 × 3 × 2}/{1 × 2 × 3} × 6 + 1$
= 80 + 90 + 24 + 1=195
In how many ways can 5 prizes be distributed among 4 boys when every boy can take one or more prizes?
Answer: (c)
First prize may be given to any one of the 4 boys, hence first prize can be distributed in 4 ways.
Similarly every one of second, third, fourth and fifth prizes can also be given in 4 ways.
∴ the number of ways of their distribution
= 4 × 4 × 4 × 4 × 4 = $4^5$ = 1024.
If two dices are tossed simultaneously, the number of elements in the resulting sample space is
Answer: (a)
Number of elements in the sample space
= 6 × 6 = 36
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
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