1Akshay has 14 toys. On his birthday his friends gave him 23 more toys. How many
toys does Akshay hav now.
Answer :-
Answers
Answer:
Let the boys get a,b,c toys. Now, a+b+c=14,a,b,c≥1 and a,b, and c are distinct.
Let a<b<c and x
1
=a,x
2
=b,x
3
=c−b. So,
3x
1
+2x
2
+x
3
=13,x
1
,x
2
,x
3
≥1
Therefore, the number of solutions is equal to the coefficient of t
14
in (t
3
+t
6
+t
9
+...)(t
2
+t
4
+...)(t+t
2
+...)
= Coefficient of t
8
in (1+t
3
+t
6
)(1+t
2
+t
4
+t
6
+t
8
)(1+t+t
2
+t...+t
8
) (neglecting higher powers)
= Coefficient of t
8
in (1+t
2
+t
3
+t
4
+t
5
+2t
6
+t
7
+2t
8
)×(1+t+t
2
+...+t
8
)
=1+1+1+1+1+2+1+2=10
Now, three distinct numbers can be assigned to three boys in 3! ways.
So, corresponding to each solution, we have six ways of distribution. So, total number of ways is 10×6=60.
Answer:
HELLO
no.of toys Akshay has =14
no.of toys Akshay got =23
Total=14+23
=37
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