Question

how many 3 digit numbers between 100 and 1000 are there whose sum of the digits is 14. solution​

Answer 1

Answer:

Your answer is : Total number of 3 digit numbers having atleast one of their digits as 7 , = (Total numbers of three digit numbers) – (Total number of 3 digit numbers in which 7 does not appear at all). = 900 – 648 = 252.

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Answer 2

Answer:

Let's count the number of digit combinations that sum to 10. To the right, we count the number of permutations.

0, 1, 9 ⟹2×2×1=4 permutations (can’t start with 0)

0, 2, 8 ⟹2×2×1=4 permutations (can’t start with 0)

0, 3, 7 ⟹2×2×1=4 permutations (can’t start with 0)

0, 4, 6 ⟹2×2×1=4 permutations (can’t start with 0)

0, 5, 5 ⟹2×2×1/2!=2 permutations (since 5 is repeated) (can’t start with 0)

1, 1, 8 ⟹3×2×1/2!=3 permutations (since 1 is repeated)

1, 2, 7 ⟹3×2×1/2!=6 permutations

1, 3, 6 ⟹3×2×1/2!=6 permutations

1, 4, 5 ⟹3×2×1/2!=6 permutations

2, 2, 6 ⟹3×2×1/2!=3 permutations (since 2 is repeated)

2, 3, 5 ⟹3×2×1/2!=6 permutations

2, 4, 4 ⟹3×2×1/2!=3 permutations (since 4 is repeated)

3, 3, 4 ⟹3×2×1/2!=3 permutations (since 3 is repeated)

If I do my arithmetic right… that makes for a total of 54 numbers.

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