Question

In a game, you roll ten dices, what is the probability that in your 10 dices exactly 2 different values come up?

Answer 1

total number of ways values appear on 10 dice =6¹⁰ (since 6 choice for each dice()

number of ways 2 different values comes on the dice =N(2 choices for each dice-number of ways only one number is shown on each dice) =2¹⁰-2

number of ways to select 2 values from 6 =C(6,2) =15

therefore total number of ways that in your 10 dices exactly 2 different values come up

=15*(2¹⁰-2)

hence probability that in your 10 dices exactly 2 different values come up =15*(2¹⁰-2)/(6¹⁰)

=0.00025353