Question

Find the probability of guessing the top three winners​ (in any​ order) from a group of 22 finalists in a spelling bee.

Answer 1

The probability is 1/9240.

There is a 1/22 chance of guessing the first one; after that, 1/21 for the second; and 1/20 the third:

(1/22)(1/21)(1/20) = 1/9240.

Answer 2

`(1)/(9240)`

Explanation:

Given : There is a group of 22 finalists in a spelling bee.

To Find: the probability of guessing the top three winners​ (in any​ order) from a group of 22 finalists in a spelling bee.

Solution:

Total finalists = 22

Winners = 3

So ,probability of guessing the first winner from a group of 22 finalists in a spelling bee =
`(1)/(22)`

Now 1 winner is selected , So, 21 finalists are remaining for the second position

So ,probability of guessing the second winner from a group of 21 finalists in a spelling bee =
`(1)/(21)`

Now 2 winners are selected . So, 20 finalists are remaining for the third position

So ,probability of guessing the third winner from a group of 20 finalists in a spelling bee =
`(1)/(20)`

So, he probability of guessing the top three winners​ (in any​ order) from a group of 22 finalists in a spelling bee :

=
`(1)/(22) * (1)/(21)* (1)/(20)`

=
`(1)/(9240)`

Hence the probability of guessing the top three winners​ (in any​ order) from a group of 22 finalists in a spelling bee is
`(1)/(9240)`