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Isaiah Farrell

Isaiah Farrell

Answered question

2022-05-29

Data set 2 3 3 4 4 4 4
I want to find the number of unique numbers of 3 digit numbers that can be formed using this.
I was thinking of doing 7 P 3 4 ! × 2 ! , but this doesn't seem right.

Answer & Explanation

Elbrinidr

Elbrinidr

Beginner2022-05-30Added 9 answers

If you have 2 as the first digit, you can have 3 and 4 as the second and third digits, so this gives 233 234 243 244, four numbers.
If you have 3 as the first digit, you can have 2 and 3 and 4 as second and third digits (but 2 only once), giving 323 332 324 342 334 343 344, seven numbers.
If you have 4 as the first digit, you can have 2, 3 and 4 as second and third digits, giving 424 442 423 432 433 434 443 444, eight numbers.
4 + 7 + 8 = 19 unique 3 digit numbers.
wanaopatays

wanaopatays

Beginner2022-05-31Added 5 answers

Alternatively, start from all 3-digit permutations of {2,3,4}, with repeats. That's 3 3 = 27. Then remove numbers that have too many 2's or 3's.
Take out numbers with exactly 2 2's: 2 choices for the remaining digit and 3 ways to permute the 3 digits is 6.
Take out numbers with exactly 3 2's, of which there's only 1.
Take out numbers with 3 3's, of which there's only 1.
Then what's left is 27-6-1-1 = 19

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