The number of ways two of these seven members can be selected is 21
The number of members of the ski patrol unit is given as:
[tex]n = 7[/tex]
The number of members of the ski patrol unit to select is given as:
[tex]r=2[/tex]
To calculate the number of ways the members can be selected, we make use of the following combination formula
[tex]^nC_r= \frac{n!}{(n-r)!r!}[/tex]
So, we have:
[tex]^7C_2= \frac{7!}{(7-2)!2!}[/tex]
Simplify the expression
[tex]^7C_2= \frac{7!}{5!2!}[/tex]
Expand each factorial
[tex]^7C_2= \frac{7 \times 6 \times 5!}{5! \times 2 \times 1}[/tex]
Cancel out the factorials
[tex]^7C_2= \frac{7 \times 6 }{2 \times 1}[/tex]
Evaluate the products
[tex]^7C_2= \frac{42}{2}[/tex]
Divide 42 by 2
[tex]^7C_2= 21[/tex]
Hence, the number of ways two of these seven members can be selected is 21
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