kajaldaryani46 wrote:
I used the same approach to solve but I think what I missed doing was breaking up the 4 digit nos into 2 parts - one less than 1500 and the other between 1500-1570.
So, I calculated the 4 digits nos that satisfy the criteria using the logic below:
1(1st digit which will be 1)* 6(ways to select from 0-5)* 3(7 cant be selected here from the 4 prime nos as the no will go beyond 1570)*4(any of the 4 prime nos can be selected).
Yes, you're right about what you need to do to correct this solution. When you're counting your choices for each digit, if you say "there are 6 choices for the hundreds digit, 0, 1, 2, 3, 4 or 5", then when you come to the tens digit, you're stuck. *If* we chose "5" for the hundreds digit, we have three choices for the tens digit (2, 3 or 5), because the number overall is less than 1570. But *if* we chose 0, 1, 2, 3 or 4 for the hundreds digit, we have four choices for the tens digit (we can use any prime, 2, 3, 5 or 7). Any time, when counting, you discover your later choices depend on which choices you made earlier, you need to either solve differently or divide the problem into cases. That's what's true here -- we don't know how many choices we have for the tens digit because it depends on what we chose for the hundreds digit.
Because you disallowed the selection of "7" in the tens place altogether, you haven't counted a lot of numbers that should be counted, like 1372 or 1277. If you divide the problem into cases (either by considering numbers from 1500-1570 separately, or by considering numbers with a tens digit of "7" separately) your approach should lead to a correct answer.
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