Let n be the total number of different 5 digit numbers that are divisible by 4. The digits comprise of 1, 2, 3, 4, 5 and 6. No digit is repeated in a number. What is the value of n?
Answer:
The divisibility test of 4 is that the tens place and units place together should be divisible by 4.
so, number of such options are 12, 16, 24, 32, 36, 52, 56, 64
now, consider a 5 digit number with 12 as the last 2 digit and the first three digits being any of the following, 3,4,5,6.
i have 4 choices for the hundredth place, 3 for the thousandth place and 2 for th ten thousandth place. So, total five digit numbers that will end with 12 would be 4 x 3 x2 = 24
Since we have 8 possibilities of choosing the last 2 numbers, therefore, the total number of 5 digits that is divisible by 4 would be
24 x 8 = 192
so, n = 192
Answer:
The divisibility test of 4 is that the tens place and units place together should be divisible by 4.
so, number of such options are 12, 16, 24, 32, 36, 52, 56, 64
now, consider a 5 digit number with 12 as the last 2 digit and the first three digits being any of the following, 3,4,5,6.
i have 4 choices for the hundredth place, 3 for the thousandth place and 2 for th ten thousandth place. So, total five digit numbers that will end with 12 would be 4 x 3 x2 = 24
Since we have 8 possibilities of choosing the last 2 numbers, therefore, the total number of 5 digits that is divisible by 4 would be
24 x 8 = 192
so, n = 192
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