00:01
Okay, it's clarissa enumerate here.
00:03
So we're going to use combination in this problem because the order of the bagels don't matter.
00:09
The repetitions allowed, so it gives us the formula c of n plus r minus 1, comma r is equal to n plus r minus 1 factorial, all over r factorial times n minus 1 factorial.
00:33
So for part a, there's eight type of bagels and we're choosing six.
00:40
So that's just n equals eight, r equals six.
00:49
That gives us c when we plug it into the formula above, 13 comma six.
00:56
And that is equal to 1 ,716.
01:03
For part b, there's eight type of bagels and we're choosing a dozen.
01:08
So n equals eight, r, equals 12.
01:14
So i'll get into the formula above.
01:16
We get 19 comma 12 which gives us 50 ,388.
01:30
For part c there's eight type of bagels and you're choosing 24 so n equals 8 r equals 24 repetitions allowed so c of 31 comma 24 which gives us 2 ,629 ,575.
02:04
And for part d, there's eight types and you're choosing a dozen, but we need at least one of each kind.
02:14
So eight of the 12 have to be one of each type of bagel.
02:19
So we're choosing four, which means 8 n is equal to 8 and our r value is 4...