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  4. The number of ways in which the letters x1, x2, ..., x10, y1, y2, ..., y15 can be arranged in a line such that the suffixes of x and those of y are in ascending order of magnitude, is

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Q. The number of ways in which the letters $x_1, x_2, ..., x_{10}, y_1, y_2, ..., y_{15}$ can be arranged in a line such that the suffixes of $x$ and those of $y$ are in ascending order of magnitude, is

Permutations and Combinations

Solution:

Since order of $x_1, x_2,..., x_{10}$ and that of $y_1, y_2,..., y_{15}$ is not to change so, $x_1, x_2, x_3,..., x_{10}$ maybe considered identical and also $y_1, y_2, .... y_{15}$. Hence, total number of required arrangements is
$\frac{25!}{10! 15!} $
$=\,{}^{25}C_{10}$
$ = \,{}^{25}C_{15} $