One problem (at most two) per thread please. Also, show your work or describe your difficulty.
Hey guys, I need help with a few questions I have to do for an assignment.
1. Radio and television stations in the USA and Canada have names that are basically four letter words. These words must begin with a K, a W, or a C and may use a blank letter as the last letter. For instance both WHO and CKLW are acceptable names.
a) How many such station names are possible?
b) How many of these are three-letter names (the last letter is a blank)?
c) How many of these names use the same letter throughout the name?
2. A bridge hand consists of 13 cards. How many bridge hands include 5 cards of one suit, 6 cards of a second, and 2 cards of a third?
Have to use combinations, permutations, or factorials for these. I don't even know where to start.
Thanks for the help in advance!
Correct for two letters. For three letters, it is necessary to use 3-permutations when letters cannot be used more than once. There is no such restriction here. So, it's 26^2 for three letters and 26^3 for four letters.
For each starting letter (W, K and C), you need consider the total number of three- and four-letter words. Then multiply the result by 3 to get the total number of possible station names.
For 2), you need to pick 3 of the 4 suits to represent your hand. How many ways can you do this?
e.g: {Club, Spade, Heart} or {Diamond, Heart, Club} (order of suits is NOT important)
The rest isn't too bad once you get this