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Question

1.Question:By using all of the digits 2,5,6,7 &9, how many odd five digit numberscan be generated

that are over sixty thousand

Answer 1

The left digit must be 6, 7 or 9

6.....right digit 5,7, or 9

7.....right digit 5 or 9

9.....right digit 5 or 7

Once you pick the right and left digits there are 3! ways to fill the remaining digits.

3*3! + 2*3! + 2*3!=7*3!=42

Answer 2

State the facts:

All five digits must be used (once each) to create a 5-digit number,

To be more than 60,000, the left digit must be 6, 7, or 9.

To be odd, the rightmost digit must be 5, 7, or 9.

When two digits are selected, the remaining 3 digits may appear in 3! = 3*2*1= 6 ways.

For 6 . . . 5, there are 6 ways.

For 6 . . . 7, there are 6 ways.

For 6 . . . 9, there are 6 ways.

For 7 . . . 5, there are 6 ways.

For 7 . . . 9, there are 6 ways.

For 9 . . . 5, there are 6 ways.

For 9 . . . 7, there are 6 ways.

That's a total of 7*6 = 42 ways.