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138 including 1 and 2 digit numbers.

-- I'll assume that we're only talking about whole numbers, and no decimals or fractions.

-- The number can't have more than 3 digits. If it had four, it would be more than 1,000.

-- One-digit numbers . . . 6 possibilities, all less than 350.

-- Two-digit numbers . . . 6 x 6 = 36 possibilities, all less than 350.

-- In three-digit numbers . . .

. . . the first digit can be 1, 2, or 3.

. . . If the first digit is 3, then the second one can be 1, 2, 3, or 4 = 4 choices.

. . . . . . For each of the 4 choices, the third digit can be 1, 2, 3, 4, 5, or 6 = 6 choices.

. . . . . . Total possibilities beginning with a 3 . . . 4 x 6 = 24

. . . If the first digit is 1 or 2, then

. . . . . . the second digit can be 1, 2, 3, 4, 5, or 6 = 6 choices. For each one . . .

. . . . . . the third digit can be 1, 2, 3, 4, 5, or 6 = 6 choices.

. . . . . . Total possibilities beginning with 1 or 2 . . . 2 x 6 x 6 = 72

Adam up:

One-digit possibilities . . . . . . . . . . . . . . . . . . . . . . 6

Two-digit possibilities. . . . . . . . . . . . . . . . . . . . . . 36

Three-digit possibilities beginning with 3. . . . . . . 24

Three-digit possibilities beginning with 1 or 2 . . . 72

Total. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

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11y ago
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11y ago

-- I'll assume that we're only talking about whole numbers, and no decimals or fractions.

-- The number can't have more than 3 digits. If it had four, it would be more than 1,000.

-- One-digit numbers . . . 6 possibilities, all less than 350.

-- Two-digit numbers . . . 6 x 6 = 36 possibilities, all less than 350.

-- In three-digit numbers . . .

. . . the first digit can be 1, 2, or 3.

. . . If the first digit is 3, then the second one can be 1, 2, 3, or 4 = 4 choices.

. . . . . . For each of the 4 choices, the third digit can be 1, 2, 3, 4, 5, or 6 = 6 choices.

. . . . . . Total possibilities beginning with a 3 . . . 4 x 6 = 24

. . . If the first digit is 1 or 2, then

. . . . . . the second digit can be 1, 2, 3, 4, 5, or 6 = 6 choices. For each one . . .

. . . . . . the third digit can be 1, 2, 3, 4, 5, or 6 = 6 choices.

. . . . . . Total possibilities beginning with 1 or 2 . . . 2 x 6 x 6 = 72

Adam up:

One-digit possibilities . . . . . . . . . . . . . . . . . . . . . . 6

Two-digit possibilities. . . . . . . . . . . . . . . . . . . . . . 36

Three-digit possibilities beginning with 3. . . . . . . 24

Three-digit possibilities beginning with 1 or 2 . . . 72

Total. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

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11y ago

138 including 1 and 2 digit numbers.

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Q: How many numbers less than 350 can be formed from 1 2 3 4 5 6 if a digit may be repeated in a number?
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