In how many ways can you change a 20 dollar bill using 10 dollar bills, 5 dollar bills, 2 dollar bills, and 1 dollar bills?
+526 Now in this problem,
Let the no. of 10 dollar bills be x, 5 dollar bills be y, 2 dollar bills be z and 1 dollar bills be w.
According to question,
\(10x+5y+2z+w=20\) \(...(1)\)
In order to find no. of ways, we've to find no. of solutions eq. (1) has.
∴ By the theory of combinatrics,
No. of solutions \(=\left( \begin{array}{c} 20+4-1 \\ 4-1 \end{array} \right)\)
\(=\left( \begin{array}{c} 23 \\ 3 \end{array} \right)\)
\(=1771\)
∴ Eq. (1) has 1771 possible set of solutions.
Thus a $20 bill can be changed in 1771 possible ways.
~Amy
+313 Each ball has five options to go
Therefore four balls will be filled in =
5×5×5×5
= 5^4 ways = 625 ways
+313 10 ca we changed into 8 different ways:-
10
5,5
5,2,2,1
2,2,2,2,1,1
2,2,2,1,1,1,1
2,2,1,1,1,1,1,1
2,1,1,1,1,1,1,1,1
8 1s
Since 10,10 counts as 1
so we know that there will be a total of 8+7 different ways to change
so your answer is 15
