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## powerangers69 3 years ago A four- digit number ( with no repetitions) is to be formed from the set of number ( 0,1,2,3,4,5,6,7). Find the probability that the number : a) is even

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1. ParthKohli

You first find the number of four-digit numbers that may be formed from the above set.

2. telliott99

Think of it this way, pick the numbers from right to left, least significant first.

3. ParthKohli

Can you do that? $8P4$ But there is something—we can't place a zero.

4. mihai

the probability is 50 %

5. powerangers69

i did 6x6x5x4 ------- 7x7x6x5 ?

6. ParthKohli

Let's think of slots. _ _ _ _ Four slots. We have 7 choices for the first(there are eight numbers in the set, but we can't place a zero). 7 for the second too(we have a zero with us the second time). 6 for the third. (We already have two numbers filled out of eight). 5 for the fourth. (We have three filled).

7. ParthKohli

We multiply $$7 \times 7 \times 6 \times 5 \Longrightarrow 49 \times 30$$

8. powerangers69

yes then? number of even numbers = 6x6x5x4 i that correct

9. ParthKohli

First find the number of four digit numbers you could make, then divide that by 2.

10. powerangers69

um answer is not 1/2 though

11. mihai

every number that ends with a 0,2,4 and 6 is an even number, so if 4 out of 8 digits give you an even number wouldn't that be 50/50?

12. telliott99

@ParthKohli see my post above. Make sense?

13. ParthKohli

Yup! That's correct!

14. powerangers69

@ParthKohli answer is given as 780/1470 not 735/1470?

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