Radio stations in a certain country use a sequence of 5 or 6 letters as their st
ID: 3031027 • Letter: R
Question
Radio stations in a certain country use a sequence of 5 or 6 letters as their station identification call letters. The first letter must be W, N, D, Q, or R. Assume there are no restrictions on the remaining letters, and repetition is allowed. How many 5-letter station identifications are possible? How many 6-letter station identifications are possible? How many total station identifications are possible? The identification for a randomly-chosen radio station is 5 letters in length. What is the probability that all five letters are different? Set up the expression that would be used to calculate the number of possible 5-letter station identifications. The expression is. (Do not simplify.) There are possible 5-letter station identifications. (Simplify your answer.) There are possible 6-letter station identifications. (Simplify your answer.) The total number of possible station identifications is. (Simplify your answer.) If the identification for a randomly-chosen radio station is 5 letters in length, then the probability that all five letters are different is. (Round to three decimal places as needed.)Explanation / Answer
a) for 5 letter station name,possible arrangement will be
As on 1 letter we can use W,N,D,Q or R, so possible ways are=4
For 2nd letter we can freely use any one of the above with or without repetition,so possible ways are 5
Similarly for 3rd ,4th and 5th letter 5 ways are there
So total no of ways should be 4×5×5×5×5=2500
B)For six letter station only limitation is on 1st letter & onwards repetition is allowed so possible no of ways are=4×5×5×5×5×5=12500
C)total station identification are sum of 5 letter & 6 letter,so total will be 2500+12500=15000
D) 5 random letter station possible ways are 5×5×5×5×5=3125
5 different letter station possible ways are 5×4×3×2×1=120
Probability of 5 different letter station name=120÷3125=0.0384
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