Groups each containing 3 boys are to be formed out of 5 boys. A, B, C, D and E such that no group can contain both C and D together. What is the maximum number of such different groups?

Permutations and Combinations 13/11/2021

A. 5
B. 6
C. 7
D. 8

Explanation:

Maximum number of such different groups = ABC, ABD,ABE, BCE,BDE,CEA,DEA =7.

Alternate method:

Total number of way in which 3 boys can be selected out of 5 is 5C3

Number of ways in which CD comes together = 3 (CDA,CDB,CDE)

Therefore, Required number of ways = 5C3 -3

= 10-3 =7.

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