Question

If A = {1, 3, 5, 7} and B = {1, 2, 3, 4, 5, 6, 7, 8}, then the number of one-to-one functions from A into B is.
(A) 1340
(B) 1860
(C) 1430
(D) 1880
(E) 1680.

Answer 1

Hint:
Find the number of elements in A and B i.e. n(A) and n(B). Thus, no. of one-one function from A into B can be find by using $${}^{n(B)}{P}_{n(A)}$$

Complete step by step solution:
Given,
A = {1, 3, 5, 7}
and, B = {1, 2, 3, 4, 5, 6, 7, 8}.
Now,
Number of elements in A and B as,
⇒ n(A) = 4 and,
⇒ n(B) = 8
Thus,
the number of one to one function from A into $$\text{B}=8_{{\text{P}}_4}$$
$$={\displaystyle \frac{8!}{4!}}$$
$$={\displaystyle \frac{8\times 7\times 6\times 5\times 4!}{4!}}$$
After dividing, we get
$$\begin{gathered} \Rightarrow 8\times 7\times 6\times 5 \\ \Rightarrow 1680 \end{gathered}$$

Note:
This type of question is counting based. For counting in maths we use permutation and combinations and factorials. factorial notation on $n$ is $n!$ and it means multiplication of natural numbers upto $n$.