# The probability of a die landing on some number n times in m throws

#### director

[Solved] The probability of a die landing on some number n times in m throws

If a die is rolled 10 times, what is the probability that it lands on '6' exactly 5 times?

My approach:
There $$\displaystyle {10 \choose 5}$$ ways for the number '6' to turn up 5 times in 10 throws.
The probability of a '6' appearing after each throw is 1/6.
The probability of any other number turning up after each throw is 5/6.

So I have,
$$\displaystyle P = {10 \choose 5} (1/6)^{5} (5/6)^{5}$$

Last edited:

#### Plato

MHF Helper
Yes that is correct.
It is simple binomal probability.

director

Thanks.