Question

The number of arrangements of the word KANGAROO in which the A's do not appear together is:

• A. 2520
• B. 3780
• C. 7650
• D. 7560

Hint:

To calculate arrangements where certain elements do not appear together, subtract the number of arrangements where they are together from the total arrangements.

Answer 1

The Correct Option is D

The word "KANGAROO" has 8 letters: K, A, N, G, A, R, O, O. The total number of arrangements without any restrictions is given by: \[ \frac{8!}{2!2!} = 2520 \] Now, we calculate the number of arrangements where the A's appear together. We treat the A's as a single unit, so the arrangement becomes K, (AA), N, G, R, O, O. The total number of such arrangements is: \[ \frac{7!}{2!} = 2520 \] Thus, the number of arrangements where the A's do not appear together is: \[ 2520 - 2520 = 7560 \] Therefore, the correct answer is 7560.