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How many combinations are possible? Assume the items are distinct.9 items chosen 7 at a time________ combinations

Sagot :

To solve this question, we use the combination formula.

The combination formula is

[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

Where n represents the amount of items in the set, and r represent the amount of items we want to select from this set.

For our problem, we have

[tex]n=9,r=7[/tex]

Then, the combinations are given by

[tex]^9C_7=\frac{9!}{7!(9-7)!}[/tex]

Solving this we have

[tex]\begin{gathered} ^9C_7=\frac{9!}{7!(9-7)!} \\ ^9C_7=\frac{9\cdot8\cdot7!}{7!(2)!} \\ ^9C_7=\frac{9\cdot8}{2!} \\ ^9C_7=\frac{9\cdot8}{2} \\ ^9C_7=9\cdot4 \\ ^9C_7=36 \end{gathered}[/tex]

We have 36 combinations.

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