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  • How many ways can 2 numbers be chosen from the set composite numbers up to 100 such that their product is a multiple of 5 and 8?  Option: 1</stron

How many ways can 2 numbers be chosen from the set composite numbers up to 100 such that their product is a multiple of 5 and 8?

 

Option: 1

4


Option: 2

8


Option: 3

0


Option: 4

1


Answers (1)

best_answer

To determine the number of ways two numbers can be chosen from the set of composite numbers up to 100 such that their product is a multiple of 5 and 8, we need to consider the factors of 5 and 8.

The composite numbers up to 100 are:

4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100

Numbers divisible by 5: 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100

Numbers divisible by 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96

To find the numbers that are multiples of 5 and 8, we need to find their common multiples.

The common multiples of 5 and 8 are: 40, 80

Now, let's count the number of composite numbers in this set that are multiples of 5 and 8.

Numbers that are multiples of 5 and 8: 40, 80

To choose two numbers from this set, we can use the formula for combinations:

\mathrm{n C r=n ! /(r !(n-r) !)}

Therefore, the number of ways to choose two numbers from the set of composite numbers up to 100 such that their product is a multiple of 5 and 8 is (2 choose 2) = 1 way.

Thus, there is 1 way to choose two numbers from the set of composite numbers up to 100 such that their product is a multiple of 5 and 8.

 

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