answer needed urgently Find the number of in which 18 identical balls can be used in 15 different cricket - Maths - Permutations and Combinations

Question

answer needed urgently

Find the number of in which 18 identical balls can be used in 15
different cricket matches please answer the question using using
multinomial theorem

ANS IS 17C3 PREVIOUSLY I SENT THE QUESTION TO THE EXPERT I GOT A
WRONG ANSWER , PLS ANS THIS QUESTION USING MULTINOMIAL THEOREM

Ajanta Trivedi · Accepted Answer

let x1 , x2 ,x3 , 
, x15 
be the number of balls used in 1st,
2nd, 3rd, 15th match
therefore
0<x1≤3 ; 0<x2≤3 , 
0<x15≤3
therefore the number of ways in which 18 identical balls can be
used in 15 matches
=coefficient of x18 in the expansion of (x+x2+x3)15=coefficient of x18 in the expansion of x15
(1+x+x2)15=coefficient of x3 in the expansion of (1+x+x2)15=coefficient of x3 in the expansion of [1-x31-x]15=coefficient of x3 in the expansion of (1-x3)15
(1-x)-15=coefficient of x3 in the expansion of (1-x3)15
1+C115x+C216x2+C317x3+ =C317

Hope this helps you