Question

A six faced dye whose faces are marked with 1, 2, 3, 4, ...... 6 is tossed n times and the list of n numbers obtained is noted down. The no. of ways exactly 3 numbers appear in the list.

• A. $3^{n} - 3.2^{n} + 3$
• B. $6C_{3}(3^{n} - 3.2^{n} + 3)$
• C. 6$\left( 3^{n} - 3.2^{n} + 3 \right)$
• D. $6C_{2}(3^{n} - 3.2^{n} + 3)$

Answer 1

Answer: (B)

$6C_{3}(3^{n} - 3.2^{n} + 3)$

Answer 2

By inclusion and exclusion principle

= $\frac{2}{6} = \frac{1}{3}$.