Permutations And Combination Mcq Model Questions & Answers, Practice Test for ibps po prelims 2024 2025

Answer: (d)

Required number of possible outcomes

= Total number of possible outcomes – Number of possible outcomes in which 5 does not appear on any dice

= $6^3 – 5^3$ = 91.

Answer: (b)

The total number of two factor products = $^200C_2$ . The number of numbers from 1 to 200 which are not multiples of 5 is 160. Therefore the total number of two factor products which are not multiple of 5 is $^160C_2$.

Hence, the required number of factors which are multiples of 5 = $^200C_2 – ^160C_2$ = 7180.

Answer: (b)

We have, $^nP_r = ^nP_{r + 1}$

⇒ ${n!}/{(n - r)!} = {n!}/{(n - r - 1)!} ⇒ 1/(n - r) = 1$

or n – r = 1 ...(1)

Also, $^nC_r = ^nC_{r – 1}$ ⇒ r + r – 1 = n

⇒ 2r – n = 1 ...(2)

Solving (1) and (2), we get r = 2 and n = 3

Answer: (a)

Two particular girls can be arranged in 2! ways and remaining 10 girls can be arranged in 10! ways. Required no. of ways = 2! × 10!

Answer: (c)

Total number of numbers without restriction = 25

Two numbers have all the digits equal.

So, the required numbers = $2^5$ – 2 = 30.