If 6 different numbers are to be selected from integers 0 to

Question

If 6 different numbers are to be selected from integers 0 to 6, how many 6-digit even integers greater than 300,000 can be composed?

Anybody with a slot method?

--- Ans will be provided later.

Thanks,
BC

Vips0000 · Answer

Why not..

Since the number must be greater than 300,000 :

first approach:
Take first number 3 or more than 3. Last number 0,2,4,6. For rest anything is fine
 = 4*7*7*7*7*4
But this includes 300,000 as well. Since we want greater than 300,000, substract this 1 possiblity.

Ans = 4*7*7*7*7*4 -1

Second approach:
Take first number 3 or more than 3. For rest anything is fine
 = 4*7*7*7*7*7
But we want only even numbers. Last digit can have 7 possible values out of which 4 are even. 
Therefore multiply above number with 4/7
Total number of intergers equal to or more than 300000 = = 4*7*7*7*7*7 *4/7

But this includes 300,000 as well. Since we want greater than 300,000, substract this 1 possiblity.

Ans = 4*7*7*7*7*7*4/7 -1

Ans = 4*7*7*7*7*4 -1

Both approaches are slot method.

Hope it helps!

Edit: Sorry dint notice. we can use only digits 0-6 not 0-9. updated.

suryanshg · Answer

since we need to select from 7 nos. i.e. 0, 1, 2, 3 ,4, 5 and 6 and find the nos. greater than 300,000.

suppose the no. to be  123456  and we are finding nos.  greater than or equal to  300,000

@position  1  - 3, 4, 5 and 6 ( we can put 4 nos.)
@positions 2, 3, 4, 5 and 6  - 0, 1, 2, 3, 4, 5 and 6 (we can put 7 nos.)

(we need to deduct 1 from the answer as the question says "find the nos. GREATER than 300,000)

Therefore, the answer is (4x7x7x7x7x7) - 1 = 67,227

Hope this helps!

MacFauz · Answer

No. of ways of choosing first digit = 4 (Greater than 2, Lesser than 7)
No. of ways of selecting last digit = 4 (Even numbers Greater than 2, Lesser than 7)
No. of ways of selecting remaining four digits = 7*7*7*7 (Lesser than 7)

So answer is 7*7*7*7*4*4 - 1 = 38415

Kudos Please... If my post helped.

suryanshg · Answer

sorry i dint see even numbers.
answer would be (4x7x7x7x7x4)-1 = 38416-1 = 38415

bellcurve · Answer

Please note the "6 different numbers" in the question; numbers cannot be repeated. If you select 4 as the first integer you can not select 4 as well as the last integer. In another words if you select even as the first number, you will only have 3 options for the last number, but if you select odd number as the first number than you will have 4 options for the last number.

If 6 different numbers are to be selected from integers 0 to

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