Question

How many numbers can you get by multiplying two or more distinct members of the set %2C2%2C3%2C5%2C11%5C%7D%24" id="TexFormula1" title="$\{1,2,3,5,11\}$" alt="$\{1,2,3,5,11\}$" align="absmiddle" class="latex-formula"> together?

Answer 1

Answer:

26

Step-by-step 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

= $\frac{5!}{2!(5-2)!}+\frac{5!}{3!(5-3)!}+\frac{5!}{4!(5-4)!}+\frac{5!}{5!(5-5)!}$

=  $\frac{5\times4\times3!}{2!3!}+\frac{5\times4\times3!}{3!\times2!}+\frac{5\times4!}{4!\times1!}+\frac{5!}{5!\times0!}$

= 10 + 10 + 5 + 1

= 26