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Six different books are given to 3 students so that every student gets at least one book. In how many ways can this be done?

Competition practicePermutations & Combinations

A729
B90
C537
D540

Step-by-Step Solution

All ways:

3^{6} = 729

. Remove those missing a student:

3 \times 2^{6} = 192

, add back those missing two:

3 \times 1 = 3.729 - 192 + 3 = 540

.

Answer: D) 540

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