Find the number of distinct numbers formed using the digits 3, 4, 5, 6

1.	Find the number of distinct numbers formed using the digits 3, 4, 5, 6, 7, 8, 9, so that odd positions are occupied by odd digits.
Answer» A number is to be formed with digits 3, 4, 5, 6, 7, 8, 9 such that odd digits always occupy the odd places. There are 4 odd digits, i.e. 3, 5, 7, 9. ∴ They can be arranged at 4 odd places among themselves in 4! = 24 ways. There are 3 even digits, i.e. 4, 6, 8. ∴ They can be arranged at 3 even places among themselves in 3! = 6 ways. ∴ Required number of numbers formed = 24 × 6 = 144

Find the number of distinct numbers formed using the digits 3, 4, 5, 6, 7, 8, 9, so that odd positions are occupied by odd digits.

Answer»

A number is to be formed with digits 3, 4, 5, 6, 7, 8, 9 such that odd digits always occupy the odd places.

There are 4 odd digits, i.e. 3, 5, 7, 9.

∴ They can be arranged at 4 odd places among themselves in 4! = 24 ways.

There are 3 even digits, i.e. 4, 6, 8.

∴ They can be arranged at 3 even places among themselves in 3! = 6 ways.

∴ Required number of numbers formed = 24 × 6 = 144