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?
Options:
A . 5
B . 6
C . 7
D . 8
Answer: Option C 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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