Question

How many numbers lie between 300 and 500 in which 4 comes only one time ?

Answer 1

They are all of the form

"4AB", "34B", and "3B4", where A nor B is 4

Case 1: The number of 3-digit numbers of type "4AB"

We can choose A as any of the 9 digits {0,1,2,3,5,6,7,8,9}
We can choose B as any of the 9 digits {0,1,2,3,5,6,7,8,9}

So there are 9×9 = 81 ways for Case 1.

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Case 2: The number of 3-digit numbers of type "34B"

We can choose B as any of the 9 digits {0,1,2,3,5,6,7,8,9}

So there are 9 ways for Case 2.

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Case 3: The number of 3-digit numbers of type "3B4"

Same as Case 2: We can choose B as any of the 9 digits {0,1,2,3,5,6,7,8,9}

So there are 9 ways for Case 2.


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Total 81+9+9 = 99

Answer 2

Given : Numbers between 300 and 500  

To Find : How many Numbers  having 4 as only once.

Solution:

300  to 500  

Break into two groups:

1st 301  to 399

2nd 400  to 499

304 , 314 ,324 , 334 , 354 , 364 , 374 , 384  , 394  =  9  

340 , 341 , 342 , 343 , 345 , 346 , 347 , 348 , 349  =  9  

9+9 = 18 numbers with one 4

400 to 499  = 100 Numbers  with one or more 4

404 , 414 ,424 , 434 , 454 , 464 , 474 , 484  , 494  =  9  

440 , 441 , 442 , 443 , 445 , 446 , 447 , 448 , 449  =  9  

18 number with 2 four

444  = 1    ,  1 number with 1 four

9+9+1 = 19 number has more than one 4  

Total Numbers = 18 + 100 - 19  

= 99  

99 Numbers  having 4 as only once.

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