The number of ways of selecting n objects out of 3n objects, of which n are alike and rest are different is -
Text Solution
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The required number of ways
= Coefficient of x n in (x 0 + x 1 + x 2 + … + x n ) (x 0 + x) 2n
= Coefficient of x n in 
(1 + x) 2n
= Coefficient of x n in (1 – x) –1 (1 + x) 2n
= Coefficient of x n in 
(1 + x) 2n
= Coefficient of x n in 
(1 + x) 2n
= Coefficient of x n in 
(1 + x) 2n
= 
Coefficient of x n–r in (1 + x) 2n = 
=
2n C n + 2n C n+1 + …. + 2n C 1 + 2n C 0
= 
[ n C r = n C n–r ]
= 
[ 2n C n + 2 2n ]
= 
= 2 2n – 1 + 
Hence is correct answer.
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