How many 3-digit numbers can be formed from first five natural no. assuming that
(a) repetition of the digits is allowed.
The first 5 natural numbers are {1,2,3,4,5}
Choose the 1st digit any of 5 ways.
Choose the 2nd digit any of 5 ways. That's 5ื5 ways to pick the 1st 2 digits
Choose the 3rd digit any of 5 ways. That's 5ื5ื5 ways to pick all 3 digits.
Answer 5ื5ื5 = 5ณ = 125 ways.
Here they all are, 12 rows of 10 and one row of 5
111 112 113 114 115 121 122 123 124 125
131 132 133 134 135 141 142 143 144 145
151 152 153 154 155 211 212 213 214 215
221 222 223 224 225 231 232 233 234 235
241 242 243 244 245 251 252 253 254 255
311 312 313 314 315 321 322 323 324 325
331 332 333 334 335 341 342 343 344 345
351 352 353 354 355 411 412 413 414 415
421 422 423 424 425 431 432 433 434 435
441 442 443 444 445 451 452 453 454 455
511 512 513 514 515 521 522 523 524 525
531 532 533 534 535 541 542 543 544 545
551 552 553 554 555
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(b) repetition of the digits is not allowed.The first 5 natural numbers are {1,2,3,4,5}
Choose the 1st digit any of 5 ways.
Choose the 2nd digit any of the 4 remaining ways.
That's 5ื4 ways to pick the 1st 2 digits
Choose the 3rd digit any of the 3 remaining ways.
That's 5ื4ื3 ways to pick all 3 digits.
Answer 5ื4ื3 = P(5,3) = 60 ways.
Here they all are, 6 rows of 10 each.
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
Edwin
