Discussion

Explanation:

Let the five digit number be 'abcde'

All digits are distinct and digits a, c and e must be odd

There are 5 odd digits i.e., 1, 3, 5, 7 and 9.
a can take any of these 5 digits in 5 ways.
c can take any of the remaining 4 digits in 4 ways.
e can take any of the remaining 3 digits in 3 ways.
∴ Number of ways of choosing values for a, c and e = 5 × 4 × 3 = 60 ways.

b and d can take distinct values out of 0, 2, 4, 6, 8 and remaining 2 odd digits in 7 × 6 = 42 ways.

∴ Total number of ways of forming the requried 5 digit number = 60 × 42 = 2520 ways.

Hence, option (c).

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