1In how many ways can n things be selected out of 3n things of which n are alike of one kind, n are alike of 2nd kind and rest are different?
how many circular bracelets can be formed using 3 red beads and 6n blue beads!
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3 Answers
11those beads can be arranged in the three following ways. 1st- all the three red beads are kept separately.2nd-two are kept together and 1 is separate.3rd- three are together.There are 6n spaces between blue beads.Fr d 1st case the no. of selecn is 1/2 6nC3 as clckws and anticlckws are not different. fr d 2nd case no. of selecn in 2*1/2*6nC2 (2 2gether are taken as 1 unit) . 2 is multiplied as 2 beads 2geder & 1 sparate are diffrnt . fr d 3rd case no. of ways is 1/2*6nC1. so d ans will be sum total of dis three.
71@ Post # 2.
It can be thought like this.
We have n alike of one kind, n alike of other kind and n different.
So total = 3n. Now since we have to select any n , it could possibly consist of :
n completely different,
n-1 n completely different and the rest 1 from either of the alike groups,
n-2 n completely different and the rest 2 from either of the alike groups..and so on..
I may be incorrect somewhere but the concept is same and after a bit thinking you should reach the result.