Counting: 4 problems on 4-digit numbers

This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 120
Joined: 02 Sep 2010
Location: India
Thanked: 7 times
GMAT Score:730

Counting: 4 problems on 4-digit numbers

by euro » Tue Oct 05, 2010 11:48 pm
[Q.1] How many 4-digit numbers can be formed by using the digits 0-9, so that no two digits are repeated?

(A) 4536 (B) 4546 (C) 4556 (D) 9436 (E) 9556



[Q.2] How many even 4-digit numbers can be formed by using the digits 0-9, so that no two digits are repeated?

(A) 2296 (B) 2396 (C) 2444 (D) 2456 (E) 2486



[Q.3] How many even 4-digit numbers divisible by 4 can be formed by using the digits 0-9, so that no two digits are repeated?

(A) 336 (B) 784 (C) 1120 (D) 1804 (E) 1936



[Q.4] How many 4-digit numbers can be formed by using the digits 0-9, so that the numbers contains exactly 3 distinct digits?

(A) 1944 (B) 3240 (C) 3850 (D) 3888 (E) 4216


For Q.1, I am getting [spoiler](A) 4536[/spoiler] as the answer.

User avatar
Master | Next Rank: 500 Posts
Posts: 270
Joined: 07 Apr 2010
Thanked: 24 times
Followed by:2 members

by neerajkumar1_1 » Wed Oct 06, 2010 1:16 am
A1) 9 * 9 * 8 * 7 = 4536
IMO: A

starting from left to right
the first digit has 9 choices i.e from 1 to 9 since the number is a 4 digit number
the rest have a option of 10 choices i.e from 0 to 9 minus the number of digits previously chosen..