Question
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?
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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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.
Was this answer helpful ?
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