Set A consists of 25 distinct numbers. We pick n numbers

Question

This is my question, so no OA just my solution.

Set A consists of 25 distinct numbers. We pick n numbers from the set A one-by-one (n<=25). What is the probability that we pick numbers in ascending order?

(1) Set A consists of even consecutive integers;
(2) n=5.

Bunuel · Accepted Answer

+1.

We should understand following two things:
1. The probability of picking any n numbers from the set of 25 distinct numbers is the same. For example if we have set of numbers from 1 to 25 inclusive, then the probability we pick n=5 numbers {3,5,1,23,25} is the same as that of we pick n=5 numbers {9,10,4,6,18}. So picking any 5 numbers  \{x_1,x_2,x_3,x_4,x_5\}  from the set is the same.

2. Now, imagine we have chosen the set  \{x_1,x_2,x_3,x_4,x_5\} , where  x_1<x_2<x_3<x_4<x_5 . We can pick this set of numbers in  5!=120  # of ways and only one of which, namely  \{x_1,x_2,x_3,x_4,x_5\}  is in ascending order. So 1 out of 120.  P=\frac{1}{n!}=\frac{1}{5!}=\frac{1}{120} .

According to the above the only thing we need to know is the size of the set (n) we are choosing from the initial set A.

Answer: B.

shalva · Answer

P = (25-n+1)/25 * 1/24 * 1/23 * . . . * 1/(25-n) If that's right, the only thing probability depends on is n. St1 is Insufficient and answer is (B) :roll:

Bunuel · Answer

The actual probability is much higher. Formula is not correct.

shalva · Answer

yes, of course, the probability is much higher. I meant the picked numbers to be consecutive, it may not be so

Bunuel · Answer

So, if B is the correct answer what's the probability then?

shalva · Answer

I've absolutely no idea

Bunuel · Answer

That is not so. But the issue you mentioned is the key part to answer the question.

janani · Answer

I think B is the right answer

this is my reasoning for the actual probability

Given 5 nos (doesn't matter what they are)
for the first choice- there is exactly one option out of 5 options. i.e we should pick the smallest of the nos. so probability is 1/5
for the second choice - again there is exactly one option i.e smallest no of the remanining for nos. so probability is 1/4
for the 3rd choice- only one smallest no of the remaining 3 nos. so probability is 1/3

and so

so total probability is 1/5*1/4*1/3*1/2*1 = 1/120

zgopal · Answer

If we pick n numbers, probability of picking in ascending order will always be  .
Explanation:
No of ways of picking n numbers from 25 (25*24*...(25-n) .. And out of that in only one all will be in ascending order.
So probability will be

Raths · Answer

let the numbers be a1 , a2 , a3 , ............, a25

Clearly option one is insufficient...Now as per option 2 (n=5)
There are 25C5 ways to select a set of 5 different numbers.
Now if we consider all the permutations of these 5 diff numbers , then only one satisfies
our criteria . Therefore out of 5! cases , only 1 is favorable and hence the probability is 1/5! = 1/120.

Therefore , the ans is B according to me.

had it been some other n<=25 , the probability would be 1/n!

cagdasgurpinar · Answer

How about this
We have a set consists of 6 numbers {1,2,3,4,5,6} and the probability that we pick 3 numbers in ascending order :
If I use your approach I will get    *    =   
but check it out
{1,2,3},{1,2,4},{1,3,4},{1,4,5},{2,3,4},{2,5,6},{3,4,5}...........

Bunuel · Answer

1/6 would be a correct answer for your example: if you continue to write 3 numbers sequences in ascending order from a set {1, 2, 3, 4, 5, 6} you'll get 20 possibilities and total # of picking 3 numbers from 6 when order matters is  P^3_6=120  -->  P=\frac{20}{120}=\frac{1}{6} .

Let's consider smaller set {1, 2, 3, 4}. What is the probability that we pick 3 numbers in ascending order?

P=Favorable scenarios/Total # of possible scenarios.

# of favorable scenarios is 4: {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, ;
Total # of possible scenarios is 24:  P^3_4=24 ;

P=\frac{# \ of \ favorable \ scenarios}{Total \ # \ of \ possible \ scenarios}=\frac{4}{24}=\frac{1}{6}  or  P=\frac{1}{3!}=\frac{1}{6} .

sudhanshushankerjha · Answer

According to my understanding, probability for option b can be calculated by: 
As we have to choose 5 among 25 so 25c5....(1)
then we can arrange those five in 5! ways..
so the outcome will be 25c2 * 5! = 25p5.
so finally out of all sets only 1 will be in ascending order, so ans = 1/(25p5)
plz correct me if i m somewhere wrong..

Bunuel · Answer

No,  P=\frac{1}{n!}=\frac{1}{5!}=\frac{1}{120}  (please see the solution above).

If we do the way you are proposed then:

Total # of outcomes =  P^5_{25}  - total # of ways to pick any 5 numbers out of 25 when order matters;
Favorable outcomes =  C^5_{25} .

P=\frac{C^5_{25}}{P^5_{25}}=\frac{1}{5!}=\frac{1}{120}

PiyushK · Answer

Why cant we calculate probability of picking 2 or 3 or 4 or 5 or ... 25 numbers in ascending order and add them all.
These are mutually exclusive cases and we can have a value for picking numbers in ascending order for any value of n.
P(2 numbers in ascending) + P(3 numbers in ascending) + P(4 numbers in ascending) ... + P(25 numbers in ascending)

I think question stem is its self sufficient to answer this question.

Bunuel · Answer

When a DS question asks to find the value, then the statement is sufficient ONLY if you can get the single numerical value.  For different n's the probability is different, thus we need to know the value of n, to get the single numerical value of the probability.

Kobe77 · Answer

Hello,

Why can't it be D?

St.1 We know that the set consists of 25 numbers. These numbers are consecutive even numbers no matter what their exact value is.
So the chances of picking the numbers in ascending order should be 1/25 * 1/24 * 1/23....1/2*1= 1/(25!)

It seems that in Statement 1 , we are not given the number of n. We could pick 4 or 5 or 25 numbers as well.

Bunuel · Answer

We should know how many numbers we are picking from 25.

hero_with_1000_faces · Answer

Bunuel

just one question, if the question wouldn't have mentioned "distinctive numbers" than "C" would have been the answer right ?

Set A consists of 25 distinct numbers. We pick n numbers

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