Question

Mark the correct alternative in the following question:

If the set A contains 7 elements and the set B contains 10 elements, then the number one-one functions from A to B is

(a) ¹⁰C₇ (b) ¹⁰C₇ $\times$ 7! (c) 7¹⁰ (d)10⁷

Answer 1

As, the number of one-one functions from A to B with m and n elements, respectively = ⁿP_m = ⁿC_m $\times$ m!

So, the number of one-one functions from A to B with 7 and 10 elements, respectively = ¹⁰P₇ = ¹⁰C₇ $\times$ 7!

Hence, the correct alternative is option (b).