If repetitions are not permitted (a) how many 3 digit number can be formed from the six digits 2,3,5,6,7 and 9? (b) how many of these are less than 400? (c) how many are even? (d) how many are odd? (e) how many are multiples of 5?

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lamanocornudaW · Accepted Answer

Step 1&amp;nbsp;(a)&amp;nbsp;There are six numbers: 2, 3, 5, 6, 7 and 9, and repetition is prohibited.Therefore, number of 3digit numbers that can be formed by these six digits will be&amp;nbsp;=6×5×4=120&amp;nbsp;(b)&amp;nbsp;The numbers less than 400 means, the digit at hundred’s place can be 2 and 3,&amp;nbsp;Since, repetition is not allowed, therefore the numbers less than 400 formed by given six digits will be&amp;nbsp;=2×5×4=40&amp;nbsp;Step 2&amp;nbsp;(c)&amp;nbsp;Since repetition is prohibited and even numbers imply that the unit place can be either 2 or 6, the following numbers will be formed by the given six digits and be considered even:=2×5×4=40&amp;nbsp;(d)&amp;nbsp;Since, odd numbers implies that the unit place can be 3,5,7 and 9, and since, repetition is not allowed, therefore the numbers that are odd and formed by given six digits will be&amp;nbsp;=4×5×4=80&amp;nbsp;Step 3&amp;nbsp;(e)&amp;nbsp;Given that repetition is prohibited and multiples of 5 will always have 5 as their unit place, the following numbers will be multiples of 5 formed by the given six digits:&amp;nbsp;=1×5×4=20

If repetitions are not permitted how many 3 digit number can be formed from the six digits 2,3,5,6,7 and 9? How many of these are less than 400?

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