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Difficulty:
45%
(medium)
Question Stats:
73% (02:33) correct
27%
(02:29)
wrong
based on 238
sessions
History
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Time
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A pizza-seller offers six kinds of toppings and two kinds of breads for its pizzas. If each pizza contains at least two kinds of toppings but not all kinds of toppings and only one kind of bread, how many different pizzas could the pizza-seller offer?
(A) 56
(B) 58
(C) 84
(D) 100
(E) 112
_________________
(A) 56
(B) 58
(C) 84
(D) 100
(E) 112
_________________
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Sometimes in GMAT combinatorics you almost need to count the possibilities in your fingers.
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Toppings Calculation
There are six kinds of toppings, and each pizza must use at least two but not all six, so exactly 2 to 5 toppings.
The number of ways to choose these is = \(6C2\) + \(6C3\) + \(6C4\)+ \(6C5\) = 15 + 20 + 15 + 6 = 56.
Bread Options
Two kinds of bread are available, with exactly one per pizza, giving 2 choices.
Total Pizzas
Multiply the toppings combinations by bread choices: 56 × 2 = 112.
ANS = A
There are six kinds of toppings, and each pizza must use at least two but not all six, so exactly 2 to 5 toppings.
The number of ways to choose these is = \(6C2\) + \(6C3\) + \(6C4\)+ \(6C5\) = 15 + 20 + 15 + 6 = 56.
Bread Options
Two kinds of bread are available, with exactly one per pizza, giving 2 choices.
Total Pizzas
Multiply the toppings combinations by bread choices: 56 × 2 = 112.
ANS = A
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