How many 3-digit numbers contain exactly one 1? examples include 510 and 771.
Answer
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1
linandrew41 1 year ago
556 response - 0 helps

Let's consider the information given:

⇒ we have a 3 digit number

⇒ it can only have one '1' within it

Let's consider the possibilities:

• first possibility: the digit '1' is in the hundreds place

⇒ 1 _ _

⇒ the tens digit has 9 choices of number 0 ⇔9 except 1

⇒ the ones digit has 9 choices of number 0⇔9 except 1

Total choices (in this case) = 9 * 9 = 81

• second possibility: the digit '1' is in the tens place

⇒ _ 1 _

⇒ the hundred digit has 8 choices '0 ⇔ 9' except 0 and 1

⇒ ones digit has 9 choices 0 ⇔ 9 except 1

Total choices (in this case) = 8 * 9 = 72

• third possibility: the digit '1' is in the ones place

⇒ _ _ 1

⇒ the hundreds digit has 8 choices 0 ⇔ 9 except 0 and 1

⇒ ones digit has 9 choices 0 ⇔ 9 except 1

Total choices (in this case) = 8 * 9 = 72

Overall Total choices =  81 + 72 + 72 = 81 + 144 = 225

Hope that helps!