Answer: 120
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Step-by-step explanation:
We have seven slots to fill. Let's call the slots A, B, C, D, E, F, G
There are 10 choices for slot A
There are 9 choices for slot B
There are 8 choices for slot C
There are 7 choices for slot D
There are 6 choices for slot E
There are 5 choices for slot F
There are 4 choices for slot G
We count down because each previous slot reduces the pool to choose from. Multiply those values out: 10*9*8*7*6*5*4 = 604800
Now divide that result by 5040. Why 5040? Because this is the number of ways to arrange 7 people within a single grouping. Note how 7! = 7*6*5*4*3*2*1 = 5040. W're dividing because order does not matter for any committee.
So we have 604800/5040 = 120 which is the answer we want
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Side note: We could use the alternate route of the nCr combination formula
nCr = (n!)/(r!*(n-r)!)
where n = 10 and r = 7