Question

In regional spelling bee, the 8 finalists consist of 3 boys and 5 girls. Find the number of sample point the sample space S for the number of possible orders at the conclusion of the contest for:

- All 8 finalist
- The fist 3 positions

Answer 1

i) There are 40320 possible orders

ii) There are 336 possible orders for the first 3 positions.

Explanation:

Given: The number of finalists = 8

The number of boys = 3

The number of girls = 5

To find the number of sample point the sample space S for the number of possible orders, we need to find factorial of 8!

The number of possible orders = 8!

= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8

= 40320

ii) From all 8 finalist, we need to choose first 3 position. Here the order is important. So we use permutation.

nPr =
`(n!)/((n - r)!)`

Here n = 8 and r = 3

Plug in n =8 and r = 3 in the above formula, we get

8P3 =
`(8!)/((8 - 3)!)`

=
`(8!)/(5!) \\= (1.2.3.4.5.6.7.8)/(1.2.3.4.5)`

= 6.7.8

= 336

So there are 336 possible orders for the first 3 positions.