Permutation and combination

[Eklav Rai]

Find how many odd 4-digit numbers less than 4000 can be made from the digits 1,2,3,4,5,6,7 if no digit may be repeated.

[Eklav Rai]

Hey reply plzzz!!

[Tutor]

The number should be less than 4000, so the first digit can be only 1, 2 and 3.
The number should be an odd number, so the last digit can be only 1, 3, 5 and 7.

The following possibilities are possible:

1 _ _ 3
1 _ _ 5
1 _ _ 7
2 _ _ 1
2 _ _ 3
2 _ _ 5
2 _ _ 7
3 _ _ 1
3 _ _ 5
3 _ _ 7

Consider the first one:
1 _ _ 3
The first blank can take any of these five numbers (2,4,5,6,7) while the second blank can only take 4 as repetition is not allowed. So the total possibilities for this one is 5x4 = 20

We have 10 such rows.

So, total possibilities = 20 * 10
                              = 200

[linu@live.com]

can u send more questions for better understanding?

[MathTutor]

The first digit can be chosen in 3 ways. (1 or 2 or 3).
The last digit can be chosen in 4 ways (1 or 3 or 5 or 7)
There are 3*4=12 ways but this include first and last digits can be 1 both or 3 both.
We exclude these 2 ways.
Therefore we are left with 12-2=10 ways.
The 2 remaining digits can be chosen from 5 possible remaining digits in 5P2. (we use Permutations because of different objects/order (no repetition is allowed))
Total of arrangements=10*5P2=200