Find the number of ways in which 12 identical coins can be distributed in 6 different purses, if not more than 3 & not less than 1 coin goes in each purse.

Step-by-step solution

Put one coin in each purse. Now 6 coins remaining. Case (i)1 coin in each of six purses =1 OOOOOO Case (ii) 2 coin in each of three purses = ^6 C ₃ 1=20 OO O O OO Case (iii) 2 coin each in two purses and 1 coin each in 2 purses = ^6 C₂ ^4 C₂=90 O O O O O O Case (iv) 2 coins in one purse and 1 coin each in 4 purses = ^6 C₁ ^5 C₄=30 O O O O O O Total =140 Alternatively: coefficient of x¹² in (x+x^2+x^3 )^6=141