Multiple choice

In how many ways can 7 persons be accommodated in 2 identical lodges, one of which can take 4 and the other 3?

  1. 25

  2. 45

  3. 35

  4. 32
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Since the lodges are identical, we are partitioning 7 people into groups of 4 and 3. The number of ways is 7C4 = 35. Because the lodges are identical, dividing by 2! is not required here because the group sizes (4 and 3) are distinct, making the partitions inherently unique.

AI explanation

The problem asks to divide 7 persons into two groups of 4 and 3, but because the lodges are identical, a group of 4 and a group of 3 is the same as a group of 3 and a group of 4. The number of ways to choose 4 persons out of 7 for the first group is 7C4, which is 35. The remaining 3 persons automatically form the second group, so there are 35 ways.

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