Hi,
13 Items: 6 ShopA 4 ShopB 3 ShopC
Choosing 3, find the number of combinations in each of the following cases.
nCr = (n!)/(r!(n - r)!). nCr on Your Caclulator
A. Choosing 3 items from the same shop: 6C3 + 4C3 + 3C3 = 20+4+1 = 25
B. Choosing 3 items which are not from shop A: 7C3 = 35
C. Choosing at least 1 item from shop A:
(6C1)(7C2) + (6C2)(7C1) + (6C3) = (6)(21) + (15)(7) + (20)
Wish You the Best in your Studies.
So we have a pool of 13 items, in all; 6 of them are from shop A; 4 are from shop B and 3 are from shop C. (C). Find the number of combinations, given that at least 1 item is from shop A. Then we have THESE 3 possible cases 1 item is from A:= 6*21 = 126 combinations 2 items are from A: = 15*7 = 105 combinations 3 items are from A: = 20 combinations. The total of these cases is + + = 126 + 105 + 20 = 251. ANSWER for part (C)