# Moderate Permutation-Combination Solved QuestionAptitude Discussion

 Q. A tea expert claims that he can easily find out whether milk or tea leaves were added first to water just by tasting the cup of tea. In order to check this claims $10$ cups of tea are prepared, $5$ in one way and $5$ in other. Find the different possible ways of presenting these $10$ cups to the expert.
 ✔ A. 252 ✖ B. 240 ✖ C. 300 ✖ D. 340

Solution:
Option(A) is correct

Since there are $5$ cups of each kind, prepared with milk or tea leaves added first, are identical.

Hence, total number of different people ways of presenting the cups to the expert is,

$=\dfrac{10!}{5!×5!}$

$= \textbf{252}$

## (1) Comment(s)

Chetan
()

My method,

10 different cups are there, let us fix the first cup, say M for milk and T for tea.

1. With first cup M

Remaining balance 9 cups, of which 4 are M and 5 are T. Hence $9C5 * 4C4$ = 126

2. With first cup T

Remaining balance 9 cups, of which 4 are T and 5 are M. Hence $9C5 * 4C4$ = 126

Total of the two $126+126 = 252$