Question

how many numbers lie between 300 and 500 in which 4 comes only one time ​

Answer 1

Answer:

For the 300–400 area, we only include numbers with 1 4 in the tens or ones place (every 10 numbers and numbers with form 34__ except 344). There are 10 numbers with 4 in the ones place (304, 314, 324, 334, 344, 354, 364, 374, 384, 394), of which 344 is excluded. Therefore, we have 9. There are 10 numbers in the 340’s, so we add them to the list, except 344, again. So we have 18 numbers from 300–400 area.

Step-by-step explanation:

For 400–500 area, we include numbers where there are no 4’s in the tens or ones place because there is already one in the hundreds place. So we have two slots, each carrying a non-four number. There are 9 possibilities for each one (0, 1, 2, 3, 5, 6, 7, 8, 9). Multiplying the number of possibilities for each slot together, we get 81. Add the two number areas together, we get 99 numbers with only 1 4.