Question
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In how many ways can 7 identical red balls, 6 identical green balls, and 1 yellow ball be put in 14 distinct boxes such that each box contains only one ball?
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Answer: Option A
:
First, the only yellow ball can be placed in one of the 14 boxes in 14C1 = 14 ways.
Out of the remaining 13 boxes, we need to choose 6 places for the 6 identical green balls. This can be done in 13C6 ways.
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:
First, the only yellow ball can be placed in one of the 14 boxes in 14C1 = 14 ways.
Out of the remaining 13 boxes, we need to choose 6 places for the 6 identical green balls. This can be done in 13C6 ways.
Therefore, the total number of ways = 14 × 13C6 = 24024
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