Question

five different letters are to be chosen from the first 10 letters of the ENGLISH alphabet. how many choices contain atleast one vowel

Answer 1

To find the number of choices that contain at least one vowel, we can use the concept of complement. First, let's find the total number of ways to choose five letters from the 10 letters of the ENGLISH alphabet. Then, let's find the number of choices that contain no vowels. To find the number of choices that contain at least one vowel, we can subtract the number of choices with no vowels from the total number of choices.

Step-by-step explanation:

To find the number of choices that contain at least one vowel, we can use the concept of complement.

First, let's find the total number of ways to choose five letters from the 10 letters of the ENGLISH alphabet. This can be represented as C(10, 5) where C is the combination formula.

Then, let's find the number of choices that contain no vowels. In this case, we can only choose from the 6 consonants in the ENGLISH alphabet. This can be represented as C(6, 5).

To find the number of choices that contain at least one vowel, we can subtract the number of choices with no vowels from the total number of choices. So the answer is C(10, 5) - C(6, 5).