Question

Nine letters are to be selected at random from the English alphabet of 26 letters. Determine the probability that 9 consonants are selected. Assume there are 21 consonants in the alphabet and that selection is to be done without replacement. Set up the problem as if it were to be solved, but do not solve.

Answer 1

To find the probability of selecting 9 consonants from the English alphabet of 26 letters, we need to calculate two combinations and divide them. First, we calculate C(26, 9) which represents the total number of ways to select 9 letters from 26. Then, we calculate C(21, 9) which represents the number of ways to select 9 consonants from 21. Finally, we divide C(21, 9) by C(26, 9) to determine the probability.

Step-by-step explanation:

To determine the probability that 9 consonants are selected from the English alphabet of 26 letters, we first need to find the total number of ways to select 9 letters from the 26 alphabet letters, which is denoted as C(26, 9). Then, we need to find the number of ways to select 9 consonants from the 21 consonants in the alphabet, denoted as C(21, 9). Finally, we divide the second value by the first value to find the probability.

C(26, 9) represents the number of combinations of 26 items taken 9 at a time, which can be calculated as 26! / (9!(26-9)!)

C(21, 9) represents the number of combinations of 21 items taken 9 at a time, which can be calculated as 21! / (9!(21-9)!)

The probability can be calculated as P = C(21, 9) / C(26, 9)