Maths doubts

[Homer Simpson]

Please explain how to do these. Thank you :)

1) At the end of the day, a bakery gives everything that is unsold to food banks for the needy. If it has 12 apple pies left at the end of a given day, in how many different ways can it distribute these pies among six food banks for the needy? Also, in how many different ways can the bakery distribute the 12 apple pies if each of the six food banks is to receive at least one pie?

2) A carton of 15 light bulbs contains one that is defective. In how many ways can an inspector choose 3 of the bulbs and get

a) one that is defective 91
b) non-defective ones 364

[Akshay Jain]

1st apple pie can go to any1 of  the 6 food banks....similarly 2nd apple pie can go to any1 of 6 diff food banks....similarly 3rd and so on
so total ways =6*6*6*6...12 times=6^12
In the 2nd part...every bank must hav atleast 1 pie...so 1st of all giv 6 pies to 6 diff banks...since all apple pies are same this can b done only in 1 way
nkw distribute the remaining six in similar way discussed in 1st part of the ques
...6*6*...6 times=6^6 is the total no. Of ways

[SINGHAM]

1.If pies are indistinguishible, then
a) 17C5
b) If at least one should be given to each, 11C5

[SINGHAM]

@Tuski, please let me know what do you mean by "not the ones that are not defective ". Thanks.

@Tuski, thanks for update.

[Ankur9]

Total bulbs = 15
Defective = 1
Non Defective = 14
a) Choose one defective bulb out of three

14C2 x 1C1 = 91

b) All are non defective

14C3 = 364

[Homer Simpson]

Thanks everyone. I got it now