How many four-digit numbers divisible by 5 can be formed using the digits 0,1,3,5,7,9 if repetition is not allowed and the digits 0 and 1 are not allowed to be placed next to each other. Note also that a number does not start with 0.
Answers
Answer:
Step-by-step explanation:
4-digit numbers, without repetition, divisible by 4, have to be formed using the digits 0,1,2,3,4,5.
Hence the last two digits of the numbers should be ending with one of these: 04, 12, 20, 32, 40, 52.
We observe that when the two numbers mentioned here have 0 in them (i.e., ending with 04, 20 and 40) we get 12 numbers each. So there are 36 numbers satisfying the given criteria.
We also observe that when the two numbers mentioned here do not have 0 in them (i.e., ending with 12,24,32 and 52) we get only 9 numbers each since 0 cannot occupy the thousands place. So there are 36 numbers satisfying the given criteria.
Hence, the number of 4-digit numbers, without repetition, divisible by 4, formed using the digits 0,1,2,3,4,5, is 36 + 36 = 72
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