a) If the order of the choices is not relevant, we need to calculate the number of combinations. We can use the formula for combinations, which is nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items being chosen. In this case, we want to choose 5 letters from 14 distinct letters without replacement, so we have:
n = 14 (total number of distinct letters)
r = 5 (number of letters being chosen)
Using the combination formula, we have:
14C5 = 14! / (5!(14-5)!) = 2002
Therefore, there are 2,002 different ways to choose 5 letters without considering the order.
(b) If the order of the choices is relevant, we need to calculate the number of permutations. We can use the formula for permutations, which is nPr = n! / (n-r)!, where n is the total number of items and r is the number of items being chosen. In this case, we want to choose 5 letters from 14 distinct letters without replacement, and the order of the choices matters, so we have:
n = 14 (total number of distinct letters)
r = 5 (number of letters being chosen)
Using the permutation formula, we have:
14P5 = 14! / (14-5)! = 14! / 9! = 14 * 13 * 12 * 11 * 10 = 240,240
Therefore, there are 240,240 different ways to choose 5 letters while considering the order.