Question 790831: how many numerals for natural numbers less than 600 can be formed by using any of the five digits 3,4,5,6, and 7 if no digits are repeats?
Answer by Edwin McCravy(20055)   (Show Source):
You can put this solution on YOUR website!
1-digit natural numbers:
There are of course 5 1-digit numbers:
3 4 5 6 7
2-digit natural numbers:
We can choose the first digit any of 5 ways.
We can choose the second digit any of the 4 remaining ways,
That's 5·4 or 20 ways
They are
34 35 36 37 43
45 46 47 53 54
56 57 63 64 65
67 73 74 75 76
Three digit numbers:
We can choose the first digit any of 3 ways, (3,4, or 5}
We can choose the second digit any of the 4 remaining ways,
We can choose the third digit any of the 3 remaining ways.
That's 3·4·3 = 36 ways.
Here they are:
345 346 347 354 356 357
364 365 367 374 375 376
435 436 437 453 456 457
463 465 467 473 475 476
534 536 537 543 546 547
563 564 567 573 574 576
Total: 5+20+36 = 61 ways
Edwin
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