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 =6^{10}
(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)
=2^{10}-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*(2^{10}-2)

hence probability that in your 10 dices exactly 2 different
values come up =15*(2^{10}-2)/(6^{10})

**=0.00025353**

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