It's not hard if you'll just think it through,
especially since you are typically good in Math. Read
what I write below carefully and you'll see
how easy it is.
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a) how many three-digit numerals can be formed?
1. We can choose the first digit any of 5 ways, {1,2,3,4,5}
2. For each of those 5 ways to choose the first digit, there are only
4 ways left to choose the second digit, since whatever we chose
for the first digit cannot be chosen again. So that's 5×4 or 20 ways
to choose just the first and second digits.
3. For each of those 20 ways to choose the first two digits, there are only
3 ways left to choose the second digit, since the two that we chose
for the first two digit cannot be chosen again. So that's 5×4×3 or 60 ways
to choose just the first, second, and third digits.
Answer: 5×4×3 = 60 ways. Here are all 60 ways:
123 124 125 132 134 135 142 143 145 152 153 154
213 214 215 231 234 235 241 243 245 251 253 254
312 314 315 321 324 325 341 342 345 351 352 354
412 413 415 421 423 425 431 432 435 451 452 453
512 513 514 521 523 524 531 532 534 541 542 543
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b) how many three-digit numerals can be formed that are odd?
In this case the last digit can only be 1,3, or 5.
1. We choose the most restrictive digit first, which is the
third or last digit.
2. We can choose the third digit any of 3 ways, {1,3,5}
3. For each of those 3 ways to chose the third digit, there are only
4 ways left to choose the first digit, since whatever we chose
for the last digit cannot be chosen again. So that's 3×4 or 12 ways
to choose just the last and first digits.
For each of those 3×4 or 12 ways to choose the last and first digits,
there are only 3 ways left to choose the second digit, since the two
that we chose for the first and last digits cannot be chosen again.
So that's 3×4×3 or 36 ways to choose just the last, first, and second
digits.
Answer: 3×4×3 = 36 ways. Here are all 36 odd numbers:
231 241 251 321 341 351 421 431 451 521 531 541
123 143 153 213 243 253 413 423 453 513 523 543
125 135 145 215 235 245 315 325 345 415 425 435
Edwin
