Best Answer

It can be done in 162 ways, viz:

1 × 20p, 1 × 10p, 1 × 5p

1 × 20p, 1 × 10p, 2 × 2p, 1 × 1p

1 × 20p, 1 × 10p, 1 × 2p, 3 × 1p

1 × 20p, 1 × 10p, 5 × 1p

1 × 20p, 3 × 5p

1 × 20p, 2 × 5p, 2 × 2p, 1 × 1p

1 × 20p, 2 × 5p, 1 × 2p, 3 × 1p

1 × 20p, 2 × 5p, 5 × 1p

1 × 20p, 1 × 5p, 5 × 2p

1 × 20p, 1 × 5p, 4 × 2p, 2 × 1p

1 × 20p, 1 × 5p, 3 × 2p, 4 × 1p

1 × 20p, 1 × 5p, 2 × 2p, 6 × 1p

1 × 20p, 1 × 5p, 1 × 2p, 8 × 1p

1 × 20p, 1 × 5p, 10 × 1p

1 × 20p, 7 × 2p, 1 × 1p

1 × 20p, 6 × 2p, 3 × 1p

1 × 20p, 5 × 2p, 5 × 1p

1 × 20p, 4 × 2p, 7 × 1p

1 × 20p, 3 × 2p, 9 × 1p

1 × 20p, 2 × 2p, 11 × 1p

1 × 20p, 1 × 2p, 13 × 1p

1 × 20p, 15 × 1p

3 × 10p, 1 × 5p

3 × 10p, 2 × 2p, 1 × 1p

3 × 10p, 1 × 2p, 3 × 1p

3 × 10p, 5 × 1p

2 × 10p, 3 × 5p

2 × 10p, 2 × 5p, 2 × 2p, 1 × 1p

2 × 10p, 2 × 5p, 1 × 2p, 3 × 1p

2 × 10p, 2 × 5p, 5 × 1p

2 × 10p, 1 × 5p, 5 × 2p

2 × 10p, 1 × 5p, 4 × 2p, 2 × 1p

2 × 10p, 1 × 5p, 3 × 2p, 4 × 1p

2 × 10p, 1 × 5p, 2 × 2p, 6 × 1p

2 × 10p, 1 × 5p, 1 × 2p, 8 × 1p

2 × 10p, 1 × 5p, 10 × 1p

2 × 10p, 7 × 2p, 1 × 1p

2 × 10p, 6 × 2p, 3 × 1p

2 × 10p, 5 × 2p, 5 × 1p

2 × 10p, 4 × 2p, 7 × 1p

2 × 10p, 3 × 2p, 9 × 1p

2 × 10p, 2 × 2p, 11 × 1p

2 × 10p, 1 × 2p, 13 × 1p

2 × 10p, 15 × 1p

1 × 10p, 5 × 5p

1 × 10p, 4 × 5p, 2 × 2p, 1 × 1p

1 × 10p, 4 × 5p, 1 × 2p, 3 × 1p

1 × 10p, 4 × 5p, 5 × 1p

1 × 10p, 3 × 5p, 5 × 2p

1 × 10p, 3 × 5p, 4 × 2p, 2 × 1p

1 × 10p, 3 × 5p, 3 × 2p, 4 × 1p

1 × 10p, 3 × 5p, 2 × 2p, 6 × 1p

1 × 10p, 3 × 5p, 1 × 2p, 8 × 1p

1 × 10p, 3 × 5p, 10 × 1p

1 × 10p, 2 × 5p, 7 × 2p, 1 × 1p

1 × 10p, 2 × 5p, 6 × 2p, 3 × 1p

1 × 10p, 2 × 5p, 5 × 2p, 5 × 1p

1 × 10p, 2 × 5p, 4 × 2p, 7 × 1p

1 × 10p, 2 × 5p, 3 × 2p, 9 × 1p

1 × 10p, 2 × 5p, 2 × 2p, 11 × 1p

1 × 10p, 2 × 5p, 1 × 2p, 13 × 1p

1 × 10p, 2 × 5p, 15 × 1p

1 × 10p, 1 × 5p, 10 × 2p

1 × 10p, 1 × 5p, 9 × 2p, 2 × 1p

1 × 10p, 1 × 5p, 8 × 2p, 4 × 1p

1 × 10p, 1 × 5p, 7 × 2p, 6 × 1p

1 × 10p, 1 × 5p, 6 × 2p, 8 × 1p

1 × 10p, 1 × 5p, 5 × 2p, 10 × 1p

1 × 10p, 1 × 5p, 4 × 2p, 12 × 1p

1 × 10p, 1 × 5p, 3 × 2p, 14 × 1p

1 × 10p, 1 × 5p, 2 × 2p, 16 × 1p

1 × 10p, 1 × 5p, 1 × 2p, 18 × 1p

1 × 10p, 1 × 5p, 20 × 1p

1 × 10p, 12 × 2p, 1 × 1p

1 × 10p, 11 × 2p, 3 × 1p

1 × 10p, 10 × 2p, 5 × 1p

1 × 10p, 9 × 2p, 7 × 1p

1 × 10p, 8 × 2p, 9 × 1p

1 × 10p, 7 × 2p, 11 × 1p

1 × 10p, 6 × 2p, 13 × 1p

1 × 10p, 5 × 2p, 15 × 1p

1 × 10p, 4 × 2p, 17 × 1p

1 × 10p, 3 × 2p, 19 × 1p

1 × 10p, 2 × 2p, 21 × 1p

1 × 10p, 1 × 2p, 23 × 1p

1 × 10p, 25 × 1p

7 × 5p

6 × 5p, 2 × 2p, 1 × 1p

6 × 5p, 1 × 2p, 3 × 1p

6 × 5p, 5 × 1p

5 × 5p, 5 × 2p

5 × 5p, 4 × 2p, 2 × 1p

5 × 5p, 3 × 2p, 4 × 1p

5 × 5p, 2 × 2p, 6 × 1p

5 × 5p, 1 × 2p, 8 × 1p

5 × 5p, 10 × 1p

4 × 5p, 7 × 2p, 1 × 1p

4 × 5p, 6 × 2p, 3 × 1p

4 × 5p, 5 × 2p, 5 × 1p

4 × 5p, 4 × 2p, 7 × 1p

4 × 5p, 3 × 2p, 9 × 1p

4 × 5p, 2 × 2p, 11 × 1p

4 × 5p, 1 × 2p, 13 × 1p

4 × 5p, 15 × 1p

3 × 5p, 10 × 2p

3 × 5p, 9 × 2p, 2 × 1p

3 × 5p, 8 × 2p, 4 × 1p

3 × 5p, 7 × 2p, 6 × 1p

3 × 5p, 6 × 2p, 8 × 1p

3 × 5p, 5 × 2p, 10 × 1p

3 × 5p, 4 × 2p, 12 × 1p

3 × 5p, 3 × 2p, 14 × 1p

3 × 5p, 2 × 2p, 16 × 1p

3 × 5p, 1 × 2p, 18 × 1p

3 × 5p, 20 × 1p

2 × 5p, 12 × 2p, 1 × 1p

2 × 5p, 11 × 2p, 3 × 1p

2 × 5p, 10 × 2p, 5 × 1p

2 × 5p, 9 × 2p, 7 × 1p

2 × 5p, 8 × 2p, 9 × 1p

2 × 5p, 7 × 2p, 11 × 1p

2 × 5p, 6 × 2p, 13 × 1p

2 × 5p, 5 × 2p, 15 × 1p

2 × 5p, 4 × 2p, 17 × 1p

2 × 5p, 3 × 2p, 19 × 1p

2 × 5p, 2 × 2p, 21 × 1p

2 × 5p, 1 × 2p, 23 × 1p

2 × 5p, 25 × 1p

1 × 5p, 15 × 2p

1 × 5p, 14 × 2p, 2 × 1p

1 × 5p, 13 × 2p, 4 × 1p

1 × 5p, 12 × 2p, 6 × 1p

1 × 5p, 11 × 2p, 8 × 1p

1 × 5p, 10 × 2p, 10 × 1p

1 × 5p, 9 × 2p, 12 × 1p

1 × 5p, 8 × 2p, 14 × 1p

1 × 5p, 7 × 2p, 16 × 1p

1 × 5p, 6 × 2p, 18 × 1p

1 × 5p, 5 × 2p, 20 × 1p

1 × 5p, 4 × 2p, 22 × 1p

1 × 5p, 3 × 2p, 24 × 1p

1 × 5p, 2 × 2p, 26 × 1p

1 × 5p, 1 × 2p, 28 × 1p

1 × 5p, 30 × 1p

17 × 2p, 1 × 1p

16 × 2p, 3 × 1p

15 × 2p, 5 × 1p

14 × 2p, 7 × 1p

13 × 2p, 9 × 1p

12 × 2p, 11 × 1p

11 × 2p, 13 × 1p

10 × 2p, 15 × 1p

9 × 2p, 17 × 1p

8 × 2p, 19 × 1p

7 × 2p, 21 × 1p

6 × 2p, 23 × 1p

5 × 2p, 25 × 1p

4 × 2p, 27 × 1p

3 × 2p, 29 × 1p

2 × 2p, 31 × 1p

1 × 2p, 33 × 1p

35 × 1p

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Q: How many ways to make 35p using 5p 10p 2p 1p and 20p coins?

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