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Need Help_P and C Problem

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by sanalnnair » Sun Sep 12, 2010 1:14 am
Hi,

Can anyone help me to solve this P and C question explaining the steps.

Source - Princeton Review

14. There are 7 types of pizza toppings that Al
can order put on his pizza: anchovies, broccoli,
extra cheese, pepperoni, eggplant, peppers, and
pineapple. Al hates the combination of anchovies
and pineapple, but loves any other combination of
toppings. How many different combinations of 3
toppings could Al order that he likes (assuming
that he orders any topping no more than once in
any given combination)?
(A) 70
(B) 60
(C) 50
(D) 35
(E) 30


Ans[spoiler] (E)
[/spoiler]
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by watchout4me » Sun Sep 12, 2010 3:00 am
E for me.

My method:

Total ways of choosing 3 toppings from 7 of them = 7 C 3 = 35

Combinations in which both anchovies and pine apple will be present = 5 (this is because you already have 2 toppings in anchovies and pine apple and can choose the third topping in 5 ways)

Hence, combinations without anchovies and pine apple together = 35 - 5 = 30
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by diebeatsthegmat » Sun Sep 12, 2010 10:33 am
sanalnnair wrote:Hi,

Can anyone help me to solve this P and C question explaining the steps.

Source - Princeton Review

14. There are 7 types of pizza toppings that Al
can order put on his pizza: anchovies, broccoli,
extra cheese, pepperoni, eggplant, peppers, and
pineapple. Al hates the combination of anchovies
and pineapple, but loves any other combination of
toppings. How many different combinations of 3
toppings could Al order that he likes (assuming
that he orders any topping no more than once in
any given combination)?
(A) 70
(B) 60
(C) 50
(D) 35
(E) 30


Ans[spoiler] (E)
[/spoiler]
because he dislike A and pineapple so 5 topping left (supposed ABCDE). select 3 from 5= 10 ways to choose 3 topping : and becasue no topping is reselected thus we only have 3 ways to arrange 3 topping thus 10*3=30
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