Let n 1 < n 2 < n 3 < n 4 < n 5 be positive integers such that n 1 + n 2 + n 3 + n 4 + n 5 = 20 . Then the number of such distinct arrangements n 1 ,   n 2 ,   n 3 ,   n 4 ,   n 5 is _________

Question

Let n 1 &#60; n 2 &#60; n 3 &#60; n 4 &#60; n 5 be positive integers such that n 1 + n 2 + n 3 + n 4 + n 5 = 20 . Then the number of such distinct arrangements n 1 , &#160; n 2 , &#160; n 3 , &#160; n 4 , &#160; n 5 is _________

Aicharya · Accepted Answer

When n 5 takes value from 10 to 6 the carry forward moves from 0 to 4 which can be arranged in 4 C 0 + 4 C 1 4 + 4 C 2 2 + 4 C 4 1 = 7 Alternate solution Possible solutions are 1, 2, 3, 4, 10 1, 2, 3, 5, 9 1, 2, 3, 6, 8 1, 2, 4, 5, 8 1, 2, 4, 6, 7 1, 3, 4, 5, 7 2, 3, 4, 5, 6 Hence 7 solutions are there.

Let n 1 < n 2 < n 3 < n 4 < n 5 be positive integers such that n 1 + n 2 + n 3 + n 4 + n 5 =…

Solution

Let n 1 &#60; n 2 &#60; n 3 &#60; n 4 &#60; n 5 be positive integers such that n 1 + n 2 + n 3 + n 4 + n 5 =…

Solution

Let n 1 < n 2 < n 3 < n 4 < n 5 be positive integers such that n 1 + n 2 + n 3 + n 4 + n 5 =…