Question

in how many ways can you choose 4 numbers from the set {1, ..., 100} such that the product is divisible by 5?

right in order for something to be divisibe by 5, it has to have one of the multiples of 5 then any other number? i tried that and i know there are 20 multiples of 5 from 1-100 then i multiplied 20 by c(100,3)? but then the answer key says it's 2705775 which isn't the same with my answer:(

Answer 1

This is
How many sets of four numbers are there in the set {1,...,100} such that the product of the four numbers is divisible by five, correct?

Answer 2

yup yup!!

Answer 3

@terenzreignz

Answer 4

it would be economical to find the combination of any four positive integers in the set such that not one of these four is a multiple of 5. Then use set complement to find the answer to the problem.

Answer 5

\(\displaystyle C(80,4)=\binom{80}{4}\)=combinations without any multiple of 5.

\(C(100,4)-C(80,4)\) = number of ways that at least one one the numbers is a multiple of 5.

Answer 6

C(100,4)−C(80,4) gives 2339645 and it's not the answer written at the back of the book :(

Answer 7

20C1*99C3

Answer 8

@sauravshakya the answer key says it's 2705775 :(

Answer 9

... any updates?

Answer 10

@oldrin.bataku none :(