Multiple choice

The number of ways in which 20 letters $ x_1,x_2,.......x_{10}, y_1, y_2, , ..... y_{10}$ be arranged in a line so that suffixes of the letters x and also those of y are respectively in ascending order of magnitude is

  1. 126

  2. 64
  3. $ 2^{20} $
  4. $ ^{20}C_{10} $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

This is a combinatorics problem. We have 20 positions. We must choose 10 positions for the x-series and 10 for the y-series. Once positions are chosen, the order is fixed (ascending). The number of ways is 20C10.

AI explanation

To arrange the 20 letters such that the suffixes of x and y remain in ascending order, we simply choose the 10 positions for the x letters out of the 20 available positions, because their internal order is fixed. Using the combination formula for selecting positions, the number of ways is 20C10. Once the x positions are chosen, the 10 y letters will fill the remaining 10 positions in their fixed ascending order. The result is 20C10.

Keep practicing — related questions