Seven friends are living in 7 different flats of an apartment. Each of them was allotted a parking slot to park their cars in the ground floor. But they used to park their cars randomly in any of the seven slots. In how many ways can they park their cars so that exactly five persons park their cars in the slots allotted to them?
A) 14
B) 21
c) 35
D) 42
E) 49
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Seven friends are living in 7 different flats of an apartmen
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alanforde800Maximus
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alanforde800Maximus
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Hi alanforde800Maximus,
We're told that seven friends are living in 7 different flats of an apartment and each was allotted a parking slot to park their cars in the ground floor; however, they used to park their cars randomly in any of the seven slots. We're asked for the number of ways that they can park their cars so that EXACTLY five persons park their cars in the slots allotted to them. While complex-looking, this question is really just a Combination Formula question.
From a conceptual level, the only way for 5 friends to park in their assigned spots and 2 friends to NOT park in their assigned spots is when the group of 2 parks in each other's spots. For example, if everyone parked in their assigned spots, we would have:
ABCDEFG
If the first 5 friends parked in their assigned spots, but the other 2 didn't, we'd have:
ABCDEGF
Thus, you can either calculate the Combination of groups of 5 from a total of 7 OR groups of 2 from a total of 7. The result would be the same:
7!/(5!)(2!) or 7!/(2)(!5!) = (7)(6)/(2)(1) = 42/2 = 21
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
We're told that seven friends are living in 7 different flats of an apartment and each was allotted a parking slot to park their cars in the ground floor; however, they used to park their cars randomly in any of the seven slots. We're asked for the number of ways that they can park their cars so that EXACTLY five persons park their cars in the slots allotted to them. While complex-looking, this question is really just a Combination Formula question.
From a conceptual level, the only way for 5 friends to park in their assigned spots and 2 friends to NOT park in their assigned spots is when the group of 2 parks in each other's spots. For example, if everyone parked in their assigned spots, we would have:
ABCDEFG
If the first 5 friends parked in their assigned spots, but the other 2 didn't, we'd have:
ABCDEGF
Thus, you can either calculate the Combination of groups of 5 from a total of 7 OR groups of 2 from a total of 7. The result would be the same:
7!/(5!)(2!) or 7!/(2)(!5!) = (7)(6)/(2)(1) = 42/2 = 21
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
