How many odd numbers from 700 to 999, inclusive, have distinct non-zer

In 1*7*4 why 7 is taken when we have 8 digits from 1 to 9 excluding the first digit?

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I counted the number of the options for the unit digit before counting options for tens digit

You can count the number of the options for the tens digit before tho, but then you have to make couple of sub-cases for each range.

1) if tens digit is even, total possible numbers = 1*4*4
2) if tens digit is odd, total possible numbers = 1*4*3

Total = 16+12=28 (same as what i got)

3 Different Scenarios using the Slot Method:

Scenario 1: 7 Digit is in the 100s Spot

the Units Digit must be Odd but can not take a 7: 1 or 3 or 5 or 9 = 4 OPTIONS

and

Tens Digit: can NOT take 0 , 7, or Digit in Units = 7 OPTIONS

Scenario 1 = 1 * 7 * 4 = 28 Numbers


Scenario 2: 8 in Hundred Spot

Units Digit: Can take any of the Odd Digits = 5 OPTIONS

and

Tends Digit: can NOT take 0, 8, nor the Digit in the Units Spot = 7 OPTIONS

1 * 7 * 5 = 35 OPTIONS



Scenario 3: 9 in the Hundreds Spot

Units Digit: can take any of the Odd Digits EXCEPT 9: 1 or 3 or 5 or 7 = 4 OPTIONS

and

Tens Digit: can NOT take 0, 9, nor the Digit in the Units Spot: 7 OPTIONS

1 * 4 * 7 = 28 NUMBERS


Scenario 1 + Scenario 2 + Scenario 3 = 28 + 35 + 28 = 91 Numbers that are ODD and have Distinct NON-Zero Digits

Answer D

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