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A chef randomly chooses 5 apples from a case of 24 apples. In how many ways can the chef make the selection?

A. in 11,628 ways
B. in 42,504 ways
C. in 5,100,480 ways
D. in 1,395,360 ways

User Lyle Z
by
4.9k points

1 Answer

2 votes

Answer:

The correct answer is B :)

Explanation:

The number of k-combinations(5) from a given set S of n (24) elements

Calculating the number of combinations

Substituting our values for n= 24 and k= 5 we get

24C5 = 24!5!(24−5)!

Subtracting 5 from 24 is 19

24!5!(19)!

Expending factorial

24X23X22X21X20X19!(5X4X3X2X1)X19!

Cancelling common factors

24X23X22X21X205X4X3X2X1

Multiply numerator values and denominator values

5100480120

Divide the 5100480 by 120

Final Result :42504.0

There are 42504.0 combinations to choose 5 items out of a set of 24

User Foreline
by
5.3k points