31) The answer is 120, found by multiplying 5 x 4 x 3 x 2 x 1 ..
this is the result of a factorial.. written as 5! meaning 5x4x3x2x1
This covers the many different combinations possible using any number of weights. (Each one only once though as the pharmacist only has one of each)
32) (32 + 27 + 33) - (26 + 26 + 21) + 21 = 40 people passed at least one class.
(32 + 27 + 33) is the number of people that passed something (we are double/triple counting)
(26 + 26 + 21) is the number of people that passed two classes, exclude these (these are the people we counted twice in the previous step.)
21 people passed all 3 classes. include this (they were removed thrice in the previous step, so we add them again)
Hey biochikaa! Thank you for your answers!! I got the same answer for 32 so that seems right. But for # 31 I got a very different answer.
My answer for 31 is:
31.
1g, 2g, 4g, 8g, and 16g = 5 weights.
Number of weights with 1 combinations = C (5,1) = 5C1, (5¦1) = 5
Number of weights with 2 combinations = C (5,2) = 5C2, (5¦2) = 10
Number of weights with 3 combinations = C (5,3) = 5C3, (5¦3) = 10
Number of weights with 4 combinations = C (5,4) = 5C4, (5¦4) = 5
Number of weights with 5 combinations = C (5,5) = 5C5, (5¦5) = 1
Total number of combinations is 5+10+10+5+1 = 31. Therefore, there are 31 different possible weights.
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