There are 252 combinations are possible with 10 initial choices and 5 decisions
Step-by-step explanation:
A combination is a selection of all or part of a set of objects, without regard to the order in which objects are selected
- nCr = [tex]\frac{n!}{r!(n-r)!}[/tex]
- n! = n(n - 1)(n - 2)(n - 3)............(1)
- n is the set of objects
- r is the selection
∵ There are 10 initial choices
∵ There are 5 decisions
- That mean chose 5 from 10
∵ repetition is allowed
∴ The number of combination is 10C5
∵ 10C5 = [tex]\frac{10!}{5!(10-5)!}[/tex]
∴ 10C5 = [tex]\frac{10!}{5!(5)!}[/tex]
∵ 5! = 5 × 4 × 3 × 2 × 1 = 120
∵ 10! = 10 × 9 × 8 × 7 × 6 × 5! = 30240 × 120
- Substitute then in 10C5
∴ 10C5 = [tex]\frac{(30240)(120)}{(120)(120)}[/tex]
∴ 10C5 = 252
There are 252 combinations are possible with 10 initial choices and 5 decisions
Learn more:
You cal learn more about combination and permutation in brainly.com/question/10525991
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