Why do MOST FILIPINOS ORDER RICE WITH DIM SUM?

The number of ways to write 10 as a sum of distinct digits, if order matters.?

• Find, with explanation, the number of ways to write 10 as a sum of distinct digits, if order matters. (Thus 2 + 3 + 5 and 3 + 5 + 2 should each be counted.) Hint: First list all the ways to write 10 as a sum of distinct digits, such as 2 + 3 + 5 = 10. (You should find that there are nine ways.) Then count the permutations of each sum separately. (For instance, there are 6 permutation of the sum 2 + 3 + 5.) I have the 9 ways to be: 1 + 9 2 + 8 3 + 7 4 + 6 1 + 2 + 7 1 + 3 + 6 1 + 4 + 5 2 + 3 + 5 3 + 5 + 2 are those right?

• Answer:

  You forgot 1+2+3+4. You wrote 2+3+5 and 3+5+2 but these use the same digits. That leaves you with: 4 pairs, which can each be written in two ways. 4x2=8. 4 triples, which can each be written in six ways. 4x6=24. 1+2+3+4, which can be written in 24 ways. 8+24+24=56