Question

How many numbers can you get by multiplying two or more distinct members of the set
`$\{1,2,3,5,11\}$` together?

Answer 1

15

Explanation:

The answer is actually 15 because 2*3*5*11, meaning 4+6+4+1, which equals 15. (This is an AOPS question, so I know this is right)

Answer 2

26

Explanation:

Data provided in the question:

set {1, 2, 3, 5, 11}

Now,

Total number of different choices of a number available = 5

Therefore,

Number of ways to choose 2 distinct numbers= ⁵C₂

Number of ways to choose 3 distinct numbers= ⁵C₃

Number of ways to choose 4 distinct numbers= ⁵C₄

Number of ways to choose 5 distinct numbers= ⁵C₅

therefore,

Total number we can get

= ⁵C₂ + ⁵C₃ + ⁵C₄ + ⁵C₅

=
`(5!)/(2!(5-2)!)+(5!)/(3!(5-3)!)+(5!)/(4!(5-4)!)+(5!)/(5!(5-5)!)`

=
`(5*4*3!)/(2!3!)+(5*4*3!)/(3!*2!)+(5*4!)/(4!*1!)+(5!)/(5!*0!)`

= 10 + 10 + 5 + 1

= 26