Challenging Counting Problem

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knight247: Legendary Member; Posts: 504; Joined: Tue Apr 19, 2011 1:40 pm; Thanked: 114 times; Followed by:11 members

Challenging Counting Problem

by knight247 » Sat Oct 15, 2011 5:26 am

If repetition of digits is not allowed, then how many 5 digit numbers begin with a digit that is prime and end with a digit that is odd?

Don't have answer options for this one. Detailed explanations would be appreciated. Thanks

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Source: Beat The GMAT — Problem Solving | Sat Oct 15, 2011 5:26 am

sam2304: Legendary Member; Posts: 1239; Joined: Tue Apr 26, 2011 6:25 am; Thanked: 233 times; Followed by:26 members; GMAT Score:680

by sam2304 » Sat Oct 15, 2011 5:43 am

Begin with even prime
1 even prime. 5 odd digits to end the number and rest to fill the remaining

_ _ _ _ _
1 8 7 6 5 = 1680

Begin with odd prime - 3 5 7
3 odd prime. 4 odd digits to end the number other than the odd prime with which it is started and rest to fill the remaining

_ _ _ _ _
3 8 7 6 4 = 4032

Total = 5712 ways.

Hope i am right. Not good at P&C