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Question
Answer the following:
How many numbers formed using the digits 3, 2, 0, 4, 3, 2, 3 exceed one million?
Solution
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.
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