there are 3 friends a,b,c they all have some 1rupee coins a has 6 and b and c have - Maths - Permutations and Combinations

Question

there are 3 friends a,b,c they all have some 1rupee coins a has
6 and b and c have 7 and 8 cons respectively they want to donate rs
10 to a trust in how many ways they can do it
pls explain using multinomial theorem and pls tell what is
multinomial theorem

Vipin Verma · Accepted Answer

Let x,y,z be number of coins denoted by a,b,c respectively
So we are given
x+y+z=10
x can range from 0-6 since a can choose 0 to 6 coins
similarly
y can range from 0-7
z can range from 0-8
The number of ways in which they can donate money
=(x0+x1+x2+x3+x4+x5+x6)(x0+x1+x2+x3+x4+x5+x6+x7)(x0+x1+x2+x3+x4+x5+x6+x7+x8)=(x7-1)(x-1)(x8-1)(x-1)(x9-1)(x-1)=(x7-1)(x8-1)(x9-1)(x-1)-3
=(1-x7)(1-x8)(1-x9)(1-x)-3
=(1-x7)(1-x8)(1-x9)(1+3c1x+4c2x2+
+12c10x10+ ) Now since they have to donate 10
rupees so we will find coefficient of x10 in above
expressio Coefficient of x10
=(12c10-5c3-4c2-3c1)
=66-10-6-3 =47 So total we have 47 ways

there are 3 friends a,b,c they all have some 1rupee coins. a has 6 and b and c have 7 and 8 cons respectively. they want to donate rs 10 to a trust . in how many ways they can do it pls explain using multinomial theorem and pls tell what is multinomial theorem.

there are 3 friends a,b,c they all have some 1rupee coins. a has 6 and b and c have 7 and 8 cons respectively. they want to donate rs 10 to a trust . in how many ways they can do it

pls explain using multinomial theorem and pls tell what is multinomial theorem.