BTGmoderatorDC wrote:A card game called "high-low" divides a deck of 52 playing cards into 2 types, "high" cards and "low" cards. There are an equal number of "high" cards and "low" cards in the deck and "high" cards are worth 2 points, while "low" cards are worth 1 point. If you draw cards one at a time, how many ways can you draw "high" and "low" cards to earn 5 points if you must draw exactly 3 "low" cards?
A. 1
B. 2
C. 3
D. 4
E. 5
Once we recognize that we can achieve 5 points by drawing 3 Low cards and 1 High card, then it really comes down to determining the number of ways to rearrange 3 L's and 1 H.
One option is to simply list the arrangements.
Alternatively, we can use the MISSISSIPPI rule, which says:
If there are n objects where A of them are alike, another B of them are alike, another C of them are alike, and so on, then the total number of possible arrangements = n!/[(A!)(B!)(C!)....]
So, for example, we can calculate the number of arrangements of the letters in MISSISSIPPI as follows:
There are
11 letters in total
There are
4 identical I's
There are
4 identical S's
There are
2 identical P's
So, the total number of possible arrangements =
11!/[(
4!)(
4!)(
2!)]
---------ONTO THE QUESTION---------------------------
Let's calculate the number of arrangements of the letters in LLLH:
There are
4 letters in total
There are
3 identical L's
So, the total number of possible arrangements =
4!/(
3!)
=
(4)(3)(2)(1)/
(3)(2)(1)
= 4
Answer: D
Cheers,
Brent
