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a) repetitions are allowed; b) repetitions not allowed

My solution: a) There are 3 cases:

  1. $3$-digit numbers;
  2. $2$-digit numbers;
  3. one digit numbers.

Case 1: $3\times 5\times5=75$

Case 2: $5\times5=25$

Case 3: $5 \times$ Sum of three cases $= 105$. (ans. key says $2253$?)

b) no repetitions:

Case 1: $3\times 4\times 3=36$

Case 2: $5\times 4=20$

Case 3: $5 \times$ Sum of cases $= 61$ (ans. key says $195$)

My answers are way different. Not sure what I'm missing. Help would be appreciated.

Zeno cosini
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Armando W
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  • There can be only 699 numbers less than 700, so maybe the question asks for the sum of the numbers formed? – user1952500 May 30 '19 at 05:17
  • is it $355+55+5$ for repetition? As $355$ is the number three digits, $55$ is the number of two digits. $5$ is the number of 1 digit. And $343+5*4+5$ for no repetition – user614287 May 30 '19 at 05:18
  • yes, that's what I get. I think the answer key may be off. I checked the question and it is as I have stated. Thanks for the responses! – Armando W May 30 '19 at 05:40

1 Answers1

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Your working out is correct for the two cases. I'm not sure exactly what the problem is -- perhaps you misread/mistranscribed the question? I'd recommend checking against just to make sure.

auscrypt
  • 8,186
  • thank you. The answer key gave 2253 for the case with repetitions, and 195 for the case with no repetitions. My answers were very different, thus the reason for asking for help. Could be the answer key is off. I checked the question and I have it correct. Thanks for clarifying. – Armando W May 30 '19 at 05:37