Question

In a regional spelling bee, the 8 finalists consist of 3 boys and 5 girls. Find the number of sample points in the sample space S for the number of possible orders at the conclusion of the contest fora. all 8 finialist.b. the first 3 positions.

Answer 1

The number of sample points in the sample space for the 8 finalists in a regional spelling bee can be determined using permutations. The number of possible orders for all 8 finalists is 40,320. The number of possible orders for the first 3 positions is 56.

Step-by-step explanation:

The number of sample points in a sample space can be found by using the concept of permutations. In this case, for the 8 finalists in the regional spelling bee, we need to determine the number of possible orders at the conclusion of the contest.

a. To find the number of possible orders for all 8 finalists, we can use the concept of factorial. There are 8 finalists in total, so the number of sample points in the sample space is 8 factorial (8!). This can be calculated as:

8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40,320

Therefore, there are 40,320 possible orders for all 8 finalists in the regional spelling bee.

b. To find the number of possible orders for the first 3 positions, we can again use the concept of factorial. There are 8 finalists in total, but we only need to consider the first 3 positions. Thus, the number of sample points in the sample space is 8 choose 3, which can be calculated as:

8 choose 3 = 8! / (3! * (8-3)!) = 8! / (3! * 5!) = 8 * 7 * 6 / (3 * 2 * 1) = 56

Therefore, there are 56 possible orders for the first 3 positions in the regional spelling bee.

Answer 2

Answer: a.) 40320

b.) 336

Step-by-step explanation:

since we have 8 possible positions, with 8 different candidates, then there are 8 possible ways of arranging the first position, 7 possible ways of arranging the Second position, 6 ways of arranging the 3rd position, 5 possible ways od arranging the 4th position, 4 possible ways of arranging the 5th position, 3 possible ways of arranging the 6th position, 2 possible ways of arranging the 7th position and just one way of arranging the 8th position since we have only one person left.

Hence, the Number of possible sample space for different 8 positions is by multiplying all the number of ways we have in our sample space which becomes:

8*7*6*5*4*3*2*1 = 40320.

b.) By the sample space we have, since we've been asked ti arrange for only the firat 3 positions, then we multiply just for the first 3ways of choosing the positions, this becomes:

8*7*6 = 336