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

In the above question, we will find the ways in which each of the pants can be paired with 9 different pieces of shirt. In this way, we can find the number of ways in which a pair can be stitched by a tailor. This is a problem based on permutations and combinations. So we have to use the concept of this.

Complete step-by-step answer:
We have been asked to find the number of ways in which a pair can be stitched by the tailor, if a man has 8 types of pant pieces and 9 types of shirt pieces.
Let us now consider the different scenarios that are possible for a tailor to stitch the pair of shirts and pants.
We know that each piece of pants can be paired with 9 different pieces of shirt.
Now, we know that there are 8 pieces of pants and by taking one piece of pant at a time, we can figure out that there are 9 ways to stitch it, since there are 9 different pieces of shirt available.
We also know that each piece of shirt can be paired with 8 different pieces of pants.
Now, we know that there are 9 pieces of shirts and by taking one piece of shirt at a time, we can figure out that there are 8 ways to stitch it, since there are 8 different pieces of pants available.
It is clear that for either of the above cases, the result will be the same.
Hence, we get that the total ways will be $\Rightarrow 8\times 9\text{ =72}$

So, the correct answer is “Option D”.

Note: In order to find the number of ways in which a pair can be stitched, sometimes we add the number of ways of selecting 8 pant pieces and 9 shirt pieces, which is equal to 17 and we choose option A, but it does not give a correct answer. Since, a pair must include a pant as well as shirt, so, we must have to multiply the number of ways of selecting 8 pant pieces and 9 shirt pieces.