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

Question

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 (A) 25C10 10! 15! (B) 25C15  (C) 25C10  (D) Both (b) and (c)

Tardigrade Admin · Accepted Answer

Since order of x1, x2,..., x10 and that of y1, y2,..., y15 is not to change so, x1, x2, x3,..., x10 maybe considered identical and also y1, y2, .... y15. Hence, total number of required arrangements is (25!/10! 15!) = 25C10 = 25C15

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

$^{25} C_{10} 10! 15!$

$^{25} C_{15}$

$^{25} C_{10}$

Both (b) and (c)

Q. 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

25C10​10!15!

25C15​

25C10​

Both (b) and (c)

Since order of x1​,x2​,...,x10​ and that of y1​,y2​,...,y15​ is not to change so, x1​,x2​,x3​,...,x10​ maybe considered identical and also y1​,y2​,....y15​. Hence, total number of required arrangements is 10!15!25!​ =25C10​ =25C15​

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

$^{25} C_{10} 10! 15!$

$^{25} C_{15}$

$^{25} C_{10}$