Mark:
5-LETTER CODE
There are 14^5 codes.
Your word contains 1, 2, 3, 4, or 5 Fs with the remaining letters coming from a set of 10.
1 F: 5 * 10^4 = 50000
2 Fs: 10 * 10^3 = 10000
3 Fs: 10 * 10^2 = 1000
4 Fs: 5 * 10 = 50
5 Fs: 1
Therefore the probability is 61051/537824 = 0.1135148
There are 14^5 = 537,824 "words" that can be formed. A, E, I are the only vowels in the first 14 letters, leaving 11 consonants, including F.
The number of words containing no vowels is 11^5 = 161,051.
The number of words containing no vowels and no F is 10^5 = 100,000.
The number of words containing F but no vowels is 161,051 - 100,000 = 61,051.
Probability is 61051 / 537824 ≈ 0.1135.
Addendum: I forgot that the F can be positioned anywhere in the word. For example, the case of one F could be Fxxxx, xFxxx, etc. Thus, there are 5 times as many ways as stated: 5 * 10,000 = 50,000.
Likewise for:
2 Fs: 5C2 = 10 ways to choose the positions for F, multiply by 1000 making a total of 10,000
3 Fs: 5C3 = 10, multiply by 100 making 1000
4 Fs: 5C4 = 5, multiplied by 10 makes 50
5 Fs: 5C5 = 1, the answer remains 1
Add them all up: 50,000 + 10,000 + 1000 + 50 + 1 = 61051. (Same as above). Phew!
TTH wrote, "
Hint on the 3 letter words = they all follow the same pattern"
How many different ways can you position the middle letter of a three letter puzzle?
Is there a state capital name that shares no letters with the name of its state
WFOREDS
MFIINNDES