Four out of 9 performers will be chosen to stand in a row on stage. How many ways can the 4 performers stand in a row?

A. 362,880 ways
B. 347,760 ways
C. 15,120 ways
D. 3,024 ways

Imagine you have 4 'slots' on the stage:

In the first one there can be 1 out of 9 performers. In the second - 1 out of 8 (because one has been already chosen). In the third - 1 out of 7 (because two have been selected). In the forth - 1 out of 6 (because three are already on the stage).
Total number of combinations is equal to: 9x8x7x6 = 3024
So the correct answer is D.
Hope it helps!

Answered by voytek | 2024-06-10

There are 3024 ways to arrange 4 performers out of 9 in a row, which is a permutation problem solved using the formula P(n, r) = n! / (n - r)!
The problem is asking to calculate the number of ways 4 performers can be arranged in a row out of 9 performers. This is a permutation problem because the order in which the performers stand matters. To solve this problem, we need to determine the number of permutations of 9 performers taken 4 at a time. The formula for permutations is given by:
P(n, r) = n! / (n - r)! where n is the total number of items to choose from, r is the number of items to choose, and ! denotes factorial.
Applying the formula:
n = 9 (total performers)
r = 4 (performers to be chosen)
P(9, 4) = 9! / (9 - 4)! = 9! / 5!
P(9, 4) = (9 x 8 x 7 x 6 x 5!) / 5!
P(9, 4) = 9 x 8 x 7 x 6
P(9, 4) = 3024
Therefore, there are 3024 ways in which the 4 performers can stand in a row on stage, which corresponds to option D.

Answered by MarlonBrando | 2024-06-24

The number of ways to arrange 4 performers out of 9 on stage is 3024. This is calculated by multiplying the available choices for each performer. Thus, the correct answer is D.
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Answered by voytek | 2025-01-29