How many different 5-person subcommittees can be formed from a club having 10 members? (A)30,240 (B) 504 (C) 2,520 (d)252

Question

anonymous · Answer

can any ine help? is integrated math

anonymous · Answer

??

amistre64 · Answer

how many ways are there to pick the first person?

amistre64 · Answer

or, if you have 10 pieces of candy in front of you; how many choices do you have on your first pick?

anonymous · Answer

10?

amistre64 · Answer

yes :)

and since youve taken 1 away, there are 9 left to choose from for the second pick ... 8 left for the 3rd pick .... you see a pattern in this yet?

anonymous · Answer

yes i do

amistre64 · Answer

this selection is called "permuation", or in street talk its just "pick"

10 pick 5 is equal to 10*9*8*7*6 , the first 5 numbers from 10

but theres a catch to this value

anonymous · Answer

so basically it will be 504 then.

amistre64 · Answer

there are groups from this pick that are "the same"  that we need to divide out

amistre64 · Answer

it would take about 120 different permuations of 5 pick 5 to show the pattern

which means that there are 120 duplications to divide out

30240/120  is what we are looking for

amistre64 · Answer

$$nCr=\frac{nPr}{r!}$$

anonymous · Answer

so it willll turn out to be 252 if its divided

amistre64 · Answer

correct