Some Probablity

amisahoo wrote:A deck of cards contains 6 cards numbered from 1 to 6. If three cards are randomly selected from the deck, what is the probability that the numbers on the cards are drawn in order ?

A. 1/60
B. 1/216
C. 1/30
D. 1/24
E. 1/6

Please help me out with this problem . Some people take it as a arrangement problem but here we are doing selection and not arrangement.

I'm assuming that the selections are without replacement and that the selection consists of card#1-card#2-card#3. We want to determine the probability that the 3 numbers are selected in ascending order (e.g., selecting 2 then 3 then 5 meets the required criteria, whereas selecting 3 then 5 then 2 does not meet the required criteria.

Notice that for any set of 3 cards, there are 3! ways in which those cards can be drawn.
For example, if 2, 3, and 5 are selected, the possible orderings are 2-3-5, 2-5-3, 3-5-2, 3-2-5, 5-2-3 and 5-3-2. Each of these 6 orderings is equally likely.

Also notice that only one of these orderings meets the criteria of the numbers selected in ascending order.

Since there are 3! (6) orderings for any selection of 3 cards, and since only 1 of those orderings will meet the required criteria, the probability is 1/6 that the numbers will be selected in ascending order.

So, the answer is E