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Akansha: Senior | Next Rank: 100 Posts; Posts: 56; Joined: Wed Sep 01, 2010 10:04 amFollowed by: 20 members; Thanked: 1 times

by Akansha » Sun May 29, 2011 10:25 am

A company assigns ID number to employees. Each is to consist of 4
different digits from 0 to 9 inclusive except 1st digit cannot be 0. How many
different combinations are there?
a. 3024
b. 4536
c. 5040
d. 9000
e. 10000

OA is B

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Source: Beat The GMAT — Problem Solving | Sun May 29, 2011 10:25 am

sameerballani: Legendary Member; Posts: 544; Joined: Mon Dec 27, 2010 8:10 amFollowed by: 2 members; Thanked: 45 times

by sameerballani » Sun May 29, 2011 10:37 am

Akansha wrote:A company assigns ID number to employees. Each is to consist of 4
different digits from 0 to 9 inclusive except 1st digit cannot be 0. How many
different combinations are there?
a. 3024
b. 4536
c. 5040
d. 9000
e. 10000

OA is B

IMO B
Let the Four digit be denoted as ABCD
For first digit A i can choose any digit other than 0 = 9 digits
For B, i can choose any digit other than the one used for A = 9 digits(We can use 0 here)
For C, i can choose any digit other than the one used for A,B = 8 Digits
For D, i can choose any digit other than the one used for A,B,C = 7 Digits

So total combinations possible = 9*9*8*7 = 4536

Thanks

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edvhou812: Master | Next Rank: 500 Posts; Posts: 143; Joined: Sat Nov 06, 2010 9:06 pmFollowed by: 1 member; Thanked: 10 times

by edvhou812 » Sun May 29, 2011 9:40 pm

I concur with sameerballani.

4 digit combo with 10 possible digits. Math would normally be 10*9*8*7. However since the first digit can't be zero, the first digit has nine possibilities, and since the second digit may include zero, the second digit will have nine possibilities. So the math will be 9*9*8*7=4,536.

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itsmebharat: Master | Next Rank: 500 Posts; Posts: 150; Joined: Tue Aug 18, 2009 7:36 amFollowed by: 2 members; Location: gurgaon; Thanked: 8 times

by itsmebharat » Sun May 29, 2011 11:51 pm

IMO B,

the ques is asking for different combinations, which you might missed while solving.

I am not an Expert, please feel free to suggest if there is an error.

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smackmartine: Legendary Member; Posts: 516; Joined: Fri Jul 31, 2009 3:22 pmFollowed by: 13 members; Thanked: 112 times

by smackmartine » Mon May 30, 2011 12:17 am

quick note on tedious multiplication in problems like this.

when you are down to 9 * 9 * 8 * 7 , try to calculate the unit digit of the product.

eg. 9*9 ---> unit digit is always 1, so deciding factor is the unit digit of the product 8*7 i.e 6

Only answer with unit digit as 6 is option B ..choose B and save precious 30 seconds for RC ;)

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sameerballani: Legendary Member; Posts: 544; Joined: Mon Dec 27, 2010 8:10 amFollowed by: 2 members; Thanked: 45 times

by sameerballani » Mon May 30, 2011 3:03 am

good point !!

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