Consider the sets and .

MATHEMATICS · Multi-part · CBSE · Mathematics · Permutations and Combinations · Permutations and Combinations

Problem

Consider the sets

A=\{a_1,a_2,a_3,a_4,a_5\}

and

B=\{b_1,b_2,\ldots ,b_7\}

. (i) Determine the total number of injective functions

f:A\to B

. (ii) Find the number of injective functions

f:A\to B

that satisfy the additional condition

f(a_1)\neq b_1

. (iii) An injective function from

A

B

is selected at random from the set calculated in part (i). Compute the probability that it satisfies

f(a_1)\neq b_1