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

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 $\text{B}={{8}_{{{\text{P}}_{4}}}}$
$=\dfrac{8!}{4!}$
$=\dfrac{8\times 7\times 6\times 5\times 4!}{4!}$
After dividing, we get
$\Rightarrow 8 \times 7 \times 6 \times 5 \\\ \Rightarrow 1680$

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 $n$.