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?
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.