A store buys 10 bottles of alcohol, including 7 bottles of

I understand the answer.

However something is confusing me when I look at it second time.

The only way 6 bottles are sold is if, We sell

1. 6 whisky
2. 5 whisky 1 Non whisky
3. 4 whisky and 2 non whisky
4. 3 whisky and 3 non whisky.


so total possible way of selling 6 bottles = 4
so total possible number when exactly 4 whiskys are sold = 1

so probabilty = 1/4

what is wrong with this equation??

Can someone explain to me why the following won't work?
i did binomial approach
P (of getting whiskey among the 10 bottles) = 7/10
P(of getting something else) = 3/10

so getting 4 whiskey out of 6:
C (6,4)*(7/10)^4*(3/10)^2

but this doesn't give me 1/2 for an answer?
help?

I guess this is simply 7C4 3C2 / 10C6 = 1/2?

Responding to a pm:

We cannot use Binomial here. Think 'flipping a coin' or 'with replacement' when you want to use binomial.
You are not replacing the bottles with identical bottles every time one of them is sold/consumed. Hence, replacement is not taking place here. The probability of selling a whiskey bottle changes after you sell one. Therefore, the probability does not stay at 7/10 so you cannot use binomial.

You have 7 W and 3 N.
So probability of selling 4 W and 2 N = (7/10)*(6/9)*(5/8)*(4/7)*(3/6)*(2/5)* 6!/4!*2!

Now, as for your question: "A box contains 100 bulbs out of which 10 are defective. A sample of 5 bulbs is drawn.The prob. that none is defective is ?"

You need to give the exact question. Did they mention whether they are replacing the bulbs after each draw? If the solution uses binomial, when you draw a bulb, you need to replace it and then draw another one. Otherwise, you cannot use binomial here.

Hi All,

Please let me know whether my approach is correct..

7C4*3C2/ 10C6 = 1/2 .

7C4- Out of 7 Whiskey bottles 4 sold
3C2 -Out of remaining 3 bottles 2 sold

10C6-- Out of 10 bottles - 6 sold.

You have used combination approach which is fine too.

Responding to a pm:



Yes, it is using the combination approach for probability. It is alright to use it because you are not arranging in both numerator and denominator. Even if you do, note that you have 10 distinct bottles. Once you select 6 bottles, the number of ways of arranging them is 6!.

So you get (7C4 * 3C2 * 6!) / (10C6 * 6!)
This is the same as 7C4*3C2 / 10C6 (the 6! anyway gets cancelled out)

If 5 or 6 bottles of whisky were sold, then it is a true statement that 4 bottles was sold (and 3, and 2, and 1). I was holping for and "selling exactly 4 whiskeys"... I always get confused on this...

No, selling 4 bottles means specifically selling exactly 4 bottles. It does not include scenarios where 5 or 6 bottles are sold. In this context, "selling 4" is understood as "selling exactly 4," not at least 4. If the scenario were to include selling 4 or more bottles, the question would typically specify "selling at least 4 whiskeys."