The total number of 3-digit numbers, whose sum of digits is 10, is ___

1.	The total number of 3-digit numbers, whose sum of digits is 10, is _______.
Answer» Let three digit number is xyz x + y + z = 10 ; x ≥ 1, y ≥ 0 z ≥ 0 ..... (1) Let T = x – 1 ⇒ x = T + 1 where T ≥ 0 Put in (1) T + y + z = 9 ; 0 ≤ T ≤ 8, 0 ≤ y, z ≤ 9 No. of non negative integral solution = ^9+3–1 C_3 –1 – 1 (when T = 9) = 55 - 1 = 54

The total number of 3-digit numbers, whose sum of digits is 10, is _______.

Answer»

Let three digit number is xyz

x + y + z = 10 ; x ≥ 1, y ≥ 0 z ≥ 0 ..... (1)

Let T = x – 1 ⇒ x = T + 1 where T ≥ 0

Put in (1)

T + y + z = 9 ; 0 ≤ T ≤ 8, 0 ≤ y, z ≤ 9

No. of non negative integral solution

= ^9+3–1 C_3 –1 – 1 (when T = 9)

= 55 - 1

= 54

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The total number of 3-digit numbers, whose sum of digits is 10, is _______.

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