SOLUTION: 5 cards are to be selected from first 10 cards numbered 1 to 10 one after the another without replacement. what is the probability that the selected numbers on the card has median

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Question 934990: 5 cards are to be selected from first 10 cards numbered 1 to 10 one after the another without replacement. what is the probability that the selected numbers on the card has median 3?
Answer by KMST(5328) About Me  (Show Source):
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The numbers on the five cards selected will be five different numbers between 1 and 10.
There are 10%2A9%2A8%2A7%2A6%2F%281%2A2%2A3%2A4%2A5%29=272 possible combinations of cards
(and sets of numbers on the cards drawn).
If one of those sets has a median of 3,
one of the cards must have the number 3,
two of the cards must have a lesser number, and
two of the cards must have a greater number.
The number less than 3 must be 1 and 2,
so we know that 3 of the cards must have the numbers 1, 2, and 3 on them.
The remaining 2 cards can have any of the other 7 possible numbers.
There are 7%2A6%2F%281%2A2%29=21 such possible sets of 2 cards,
so for 21 of the 252 possible sets of cards would the median of the numbers on the cards be 3.
The probability that the set of numbers on the selected cards has a median of 3 is
21%2F252=highlight%281%2F12%29
How many of those