Free Practice Question
PS · Problem Solving
705-805
Combinations
In how many ways can one divide twelve different chocolate bars equally among four boys?
Answer Choices
Correct answer marked belowA
12!/3!
B
12!/4!
12!/(3!)^4
Correct
D
12!/(4!)^3
E
12!/(3!4!)
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Official Explanation
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Official Solution Credit: Veritas Prep
You need to divide 12 chocolate bars among four boys i.e. you have to make four distinct groups.
To boy 1, you can give the first chocolate in 12 ways, the second chocolate in 11 ways and the third chocolate in 10 ways. But we don’t want to arrange the chocolates so you can select 3 chocolates for boy 1 in ways (this is equivalent to if you follow the formula).
Similarly, you can select 3 chocolates for the second boy in ways (i.e. ), for the third boy in ways (i.e. ) and for the fourth boy in ways (i.e. )…
Official Solution Credit: Veritas Prep
You need to divide 12 chocolate bars among four boys i.e. you have to make four distinct groups.
To boy 1, you can give the first chocolate in 12 ways, the second chocolate in 11 ways and the third chocolate in 10 ways. But we don’t want to arrange the chocolates so you can select 3 chocolates for boy 1 in ways (this is equivalent to if you follow the formula).
Similarly, you can select 3 chocolates for the second boy in ways (i.e. ), for the third boy in ways (i.e. ) and for the fourth boy in ways (i.e. )…
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What it tests
Whether you can count arrangements and selections correctly — permutations vs. combinations.
Common trap
Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.
Details
Difficulty
705-805
Type
PS
Category