In how many ways can we write 20 as a sum of 3 non-negative integer?
Answers
1+8+11
2+4+14
is the answer
Answer: The required number of ways is 25.
Step-by-step explanation: We are given to find the number of ways in which 20 can be written as a sum of 3 non-negative integers.
The partitions of 20 in 3 non-negative integers are
(1) 20 = 18 + 1 + 1,
(2) 20 = 17 + 2 + 1,
(3) 20 = 16 + 3 + 1,
(4) 20 = 16 + 2 + 2,
(5) 20 = 15 + 4 + 1,
(6) 20 = 15 + 3 + 2,
(7) 20 = 14 + 5 + 1,
(8) 20 = 14 + 4 + 2,
(9) 20 = 14 + 3 + 3,
(10) 20 = 13 + 6 + 1,
(11) 20 = 13 + 5 + 2,
(12) 20 = 13 + 4 + 3,
(13) 20 = 12 + 7 + 1,
(14) 20 = 12 + 6 + 2,
(15) 20 = 12 + 5 + 3,
(16) 20 = 12 + 4 + 4,
(17) 20 = 11 + 8 + 1,
(18) 20 = 11 + 7 + 2,
(19) 20 = 11 + 6 + 3,
(20) 20 = 11 + 5 + 4,
(21) 20 = 10 + 9 +1,
(22) 20 = 10 + 8 +2,
(23) 20 = 10 + 7 + 3,
(24) 20 = 10 + 6 + 4,
(25) 20 = 10 + 5 + 5 .
So, we can write 20 as a sum of 3 non-negative integers in 25 ways.
Thus, the required number of ways is 25.