Kenneth Rosen Ex 5.5 closed

Question

Suppose that a family has 14 children, including two sets of identical triplets, three sets of identical twins, and two individual children.How many ways are there to seat these children in a row of chairs if the identical triplets or twins cannot be distinguished from one another?

Comments

302702400 ??

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Yes, correct. Can you explain?

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let we have children like,

a, a, a, b, b, b, c, c, d, d, e, e, x, y    // 2 triplets(a,b) , 3 twins(c,d,e),  2 individuals(x,y)

now, problem is to arrange all the above numbers considering duplicates

= $\frac{14!}{3!*3!*2!*2!*2!}$ = 302702400