amsm25 wrote:There are 7 type of pizza toppings that Al can order put on his pizza:A,B,C,D,E,F,G. Al hates the combination of A and G. How many different combinations of 3 topping could Al order that he likes(assuming that he orders any toppings no more than once in any given combination)
1)70
2)60
3)50
4)35
5)30
AO- 5)30.
Good combinations = total possible combinations - bad combinations.
Total possible combinations:
Number of options for the first topping = 7.
Number of options for the second topping = 6.
Number of options for the third topping = 5.
To combine these options, we multiply:
7*6*5.
The product above represents the number of ways that the 3 toppings can be ARRANGED: ABC, CAB, etc.
But here we need to count the number of ways that the 3 toppings can be COMBINED.
In a combination, the ORDER of the toppings doesn't matter: ABC is the same combination as CAB.
So that we don't overcount these duplicate combinations, we must divide by the number of ways to arrange 3 elements:
3! = 3*2*1.
Thus:
The number of combinations of 3 toppings that can be formed from 7 options = (7*6*5)/(3*2*1) = 35.
But among these 35 combinations are those that include both A and G.
These bad combinations must be subtracted from the total.
Thus, the correct answer must be less than 35.
The correct answer is
E.
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