Question

Answer the following:

How many numbers formed using the digits 3, 2, 0, 4, 3, 2, 3 exceed one million?

Answer 1

A number that exceeds one million is to be formed from the digits 3, 2, 0, 4, 3, 2, 3.

Then the numbers should be any number of 7 digits that can be formed from these digits.

Also among the given numbers 2 is repeated twice and 3 is repeated thrice.

∴ Required number of numbers = Total number of arrangements possible among these digits – number of arrangements of 7 digits which begin with 0.

= `(7!)/(2!3!) - (6!)/(2!3!)`

= `(7 xx 6 xx 5 xx 4 xx 3!)/(2 xx 3!) – (6 xx 5 xx 4 xx 3!)/(2 xx 3!)`

= 7 × 6 × 5 × 2 – 6 × 5 × 2

= 6 × 5 × 2(7 – 1)

= 60 × 6

= 360

∴ 360 numbers that exceed one million can be formed with the digits 3, 2, 0, 4, 3, 2, 3.