Question

On a certain committee there are 7 senators. Three of these members will be chosen to form a subcommittee. How many possible subcommittees are there?

Answer 1

you are being asked for "7 choose 3" or \(\binom{7}{3}\)
do you know how to compute it ?

Answer 2

No, and we can't use any calcualtors

Answer 3

it is not hard
make a fraction
on the top put 3 whole numbers starting and 7 and counting down
in the bottom, put \(3!=3\times 2\)

Answer 4

you get
\[\frac{7\times 6\times 5}{3\times 2}\] cancel first, multiply last

Answer 5

I understand the concept behind the numerator but i don't understand why the denominator is what it is...

Answer 6

because if you just compute
\[7\times 6\times 5\] that counts choosing senators A, B, C
different from choosing
A, C, B
B, A, C
B, C, A
C, A, B
C, B, A

i.e. it counts each selection 6 times, the number of ways you can arrange 3 senators
so you have to divide by 6

Answer 7

similarly for example
\[\binom{10}{4}=\frac{10\times 9\times 8\times 7}{4\times 3\times 2}\]

Answer 8

Ok so the way to find the denominator for this type of problem you just multiply the number your choosing by each descending whole number down to 1?

Answer 9

yes, that is called "factorial"

Answer 10

ok, thank you so much!

Answer 11

don't forget that the answer to "how many?" is always a whole number, so cancel first multiply last
there will never be a fraction when you are done, onlyi a whole number

Answer 12

yw