in Combinatory edited by
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5 votes
5 votes

How many strings of $5$ digits have the property that the sum of their digits is $7$?

  1. $66$
  2. $330$
  3. $495$
  4. $99$
in Combinatory edited by
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2 Answers

6 votes
6 votes
Best answer

Let five digit A, B, C, D, E then A + B + C + D + E = 7

given n = 7, r = 5 we know that

n + r – 1 C  r - 1  = 7+5 -1 C 5-1 = 11 C 4 = 11x 10x9x8/1x2x3x4 =330

Answer B

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3 Comments

Let five digit A, B, C, D, E then A + B + C + D + E = 7

If A is 0 then it won't be 5 digit string.So, we consider this too..

Tell me if I am wrong..
1
1
It's saying "strings", not numbers... I think that's the catch
3
3
can someone give context for the formula used here. how is it used?’
0
0
0 votes
0 votes
This simple star-bar problem with IODB template where the a+b+c+d+e=7 which is equivalent to Combination with repitition, where content does not matters only order matters.

 

THere are 7 stars and 4 bars. (7+4)C4==330
Answer:

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