Solution to A person has 8 children of them he takes 3 at a time to a … - Sikademy
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Archangel Macsika

A person has 8 children of them he takes 3 at a time to a circus. He does not take the same three children twice to the circus. How many times he will have to go to circus to ensure that every three children have seen the circus together? In this case find the number of times a particular child has visited the circus. From 8 men and 4 women and team of 5 is to be formed. In how many ways can this be done so as to include at least one woman?

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No 3 same children taken again required number = ^{8}C_3=\frac{8!}{3!.5!}=56

Total number of men =8 

Total number of women =4 

Team = 5 persons → at least 1 women 

Case 1→1 women + 4 men ⇒^4C_1 \times ^{8}C_4=4\times70=280

Case 2→2 women + 3 men ⇒ ^4C_2 \times ^{8}C_3=6\times56=336

Case 3→ 3 women + 2 men ⇒^4C_3 \times ^{8}C_2=4\times28=112

Case 4→ 4 women + 1 men ⇒^4C_4 \times ^{8}C_1=1\times8=8

Total ways =280+336+112+8=736

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Question ID: mtid-5-stid-8-sqid-484-qpid-371