Divide into groups

Of 3n+1 objects, n are indistinguishable, and the remaining ones are distinct. Find the number of ways to choose n objects from them.

2 Answers

2305
Shaswata Roy ·

Is it-3n+1Cn+3n+1Cn-1+3n+1Cn-2+.....+3n+1C0

2305
Shaswata Roy ·

If No. of indistinguishable objects = 0,#ways to select n objects = 2n+1Cn

If No. of indistinguishable objects = 1,#ways to select rest of the objects = 2n+1Cn-1

If No. of indistinguishable objects = 2,#ways to select rest of the objects = 2n+1Cn-2

Hence the # ways is = 2n+1Cn+ 2n+1Cn-1+ 2n+1Cn-2.....2n+1C0

Since this no. is equal to 2n+1Cn+ 2n+1Cn+1+ 2n+1Cn+2.....2n+1C2n+1

Therefore answer is = 2n+1C0+ 2n+1C1+ 2n+1C2.....2n+1C2n+12 = 2n+1/2 = 2n

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