In the 6-digit integer 543, 2xy, x, and y are chosen from the digits

Question

In the 6-digit integer 543, 2xy, x, and y are chosen from the digits 0, 2, 4, 6, and 8. What is the probability that 543, 2xy is divisible by 8?

A.  \frac{1}{5}

B.  \frac{6}{25}

C.  \frac{7}{25}

D.  \frac{8}{25}

E.  \frac{9}{25}

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PranavVyas · Answer

200 (x=0, y=0)
208 (x=0, y=8)
240 (x=4, y=0)
248 (x=4, y=8)
280 (x=8, y=0)
288 (x=8, y=8)
there will be 6 combinations that make “2xy” divisible by 8.
5 digits {0, 2, 4, 6, 8}. there are a total of 5 * 5 = 25 possible

IMO- B (6/25)

Oppenheimer1945 · Answer

00
08

40
48

24
64

80
88

P=8/25

albert_jokelin · Answer

Given a 6-digit integer, 543,2xy. Where x & y E {0, 2, 4, 6, 8}.

The total number of ways we can arrange them is 5 * 5 = 25.

For a number to be divisible by 8, the last three digits should be divisible by 8. 
=> 2xy must be divisible by 8. Of the given set,  we can have 9 values (00, 08, 24, 40, 48, 60, 68, 80, 88)  we can have 8 values (00, 08, 24, 40, 48, 64, 80, 88).

Therefore, P(2xy divisible by 8) = 8/25. IMO is Option D.

chiplesschap · Answer

Total outcomes of x & y -> 5 x 5 -> 25
Favourable outcomes - 00 + multiples of 8, so possible favourable outcomes are : 00, 08, 24, 40, 48, 64, 80, 88 -> 8

Hence answer has to be D -> 8/25

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Shubhradeep · Answer

Correct option should be Option D

We should first know the divisibility rule by 8.

It says, if for any number, the last three digits are divisible by 8, the complete number is divisible by 8. For example, we take a number  35720 . In this,  the last 3 digits make the number 720 which is divisible by 8, so 35720 will be divisible by 8.

On the other hand, 35730 will not be divisible by 8 because 730 is not divisible by 8.

In our case, we have 0,2,4,6,8 as the choices for the last 2 digits. First let us see how many ways we can have for the last 2 digits. There is no restriction for repetition of digits. So we can have 5*5 = 25 ways for the last 2 digits.

From them some of the combinations would be divisible by 8, which are

2  00  
 2  08  
 2  24  
 2  40  
 2  48  
 2  64  
 2  80  
 2  88

So total 8 possibilities.

Probability = 8/25

Hence, answer should be D

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In the 6-digit integer 543, 2xy, x, and y are chosen from the digits

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In the 6-digit integer 543, 2xy, x, and y are chosen from the digits

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