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Question
How many numbers of six digits can be formed from the digits 0, 1, 3, 5, 7 and 9 when no digit is repeated? How many of them are divisible by 10 ?
Solution
The first digit of the number cannot be zero. Thus, it can be filled in 5 ways.
The number of ways of filling the second digit = 5
(as the repetition of digits is not allowed)
The number of ways of filling the third digit = 4
The number of ways of filling the fourth digit = 3
The number of ways of filling the fifth digit = 2
The number of ways of filling the sixth digit = 1
∴ Required numbers =`5xx5xx4xx3xx2xx1=600`
For the number to be divisible by 10, the sixth digit has to be zero.
Now, the first digit can be filled in 5 ways.
Number of ways of filling the second digit = 4
Number of ways of filling the third digit = 3
Number of ways of filling the fourth digit = 2
Number of ways of filling the fifth digit = 1
Number of ways of filling the sixth digit = 1
Total numbers divisible by 10 =`5xx4xx3xx2xx1xx1=120`
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