Question

A bag contains 7 apples and 5 oranges. if you select 6 pieces of fruit without looking, how many ways can you get exactly 5 apples?

Answer 1

[We assume that each piece of apple is identical]

{{{{This part for little more explanation:

There are 12C6 ways that 6 fruits can be taken from the bag

which is equal to

=12!/{(12-6)!*6!}

=(12*11*10*9*8*7*6!) / (6!*6!)

=665280 / (6*5*4*3*2*1)

=924 ways

}}}}}

Your main solution here:

Similarly there are 6C5 ways to get exactly 5 apples out of 6 fruits which is equal to,

=6! / {(6-5)! *5! }

=(6*5!) / (1!*5!)

=6 ways>>>>>>>ANSWER

NOTE: nCx=n! / [(n-x)! *x!]  where n=total items and x= no of items choosen

{n is written up in the upper left of C and x is written as Subscript}