Question

There are $8$ types of pant pieces and $9$ types of shirt pieces with a man. The number of ways in which a pair ($1$ pant, $1$ shirt) can be stitched by the tailor is
A) $17$
B) $56$
C) $64$
D) $72$

Answer 1

There are $8$ types of pant pieces. So for every shirt piece, there are $8$ possible ways to make a unique outfit. There are $9$ types of shirt pieces. A man can wear each shirt with one pant only. So multiply the number of pants with the number of shirts to get the answer.

Complete step-by-step answer:
Given, number of pant pieces= $8$
Number of shirt pieces= $9$
We have to find the number of ways in which a pair ($1$ pant, $1$ shirt) can be stitched by the tailor.
This is a question of permutation and combination, which can be solved by using a table, a tree diagram or using the Fundamental Counting Principle.
Here we can solve this question by Fundamental Counting Principle which explains how you can find the total number of outcomes for multiple experiments by multiplying the number of outcomes for each separate experiment.
So, we just need to multiply the number of pants with the number of shirts to get the answer.
$8 \times 9 = 72$
So there are $72$ ways in which a pair ($1$ pant, $1$ shirt) can be stitched by the tailor.

Hence, option (D) is the correct answer.

Note: This question can also be do by following method:
Ways in which a pair ($1$ pant, $1$ shirt) can be stitched by the tailor = Ways to select $1$ pant piece out of $8$ pant pieces $\times$ Ways to select $1$ shirt piece out of $9$ shirt pieces = ${}^8{C_1} \times {}^9{C_1} = 8 \times 9 = 72$.