Nell made a secret code. Each code word has 2 letters. Each word begins with a consonant and ends with a vowel. How many code words can Nell make with 3 consonants and 2 vowels?
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To find out how many code words Nell can make, we need to consider the number of choices she has for each position.
First, we know that each word has 2 letters, so we need to choose 2 positions.
Now, let's consider the first position. Nell has 3 consonants to choose from, as she needs a consonant at the beginning of the word.
For the second position, she has 2 vowels to choose from since she needs a vowel at the end of the word.
To find the total number of code words, we multiply the number of choices for each position.
Number of choices for the first position: 3 (consonants)
Number of choices for the second position: 2 (vowels)
Total number of code words = Number of choices for the first position * Number of choices for the second position
Total number of code words = 3 * 2 = 6
Nell can make 6 code words with 3 consonants and 2 vowels.
To find out how many code words Nell can make, we need to determine the number of choices she has for each position in the code word.
Step 1: Determine the choices for the first letter:
Since the first letter must be a consonant, and Nell has 3 consonants to choose from, there are 3 choices for the first letter.
Step 2: Determine the choices for the second letter:
Since the second letter must be a vowel, and Nell has 2 vowels to choose from, there are 2 choices for the second letter.
Step 3: Determine the choices for the third letter:
The third letter must also be a consonant, and Nell has used one consonant already, so there are now only 2 consonants left to choose from.
Step 4: Determine the choices for the fourth letter:
The fourth letter must be a vowel, and Nell has used one vowel already, so there is now only 1 vowel left to choose from.
Step 5: Determine the choices for the fifth letter:
Again, the fifth letter must be a consonant, and Nell has used two consonants already, so there is now only 1 consonant left to choose from.
Now, multiply the number of choices for each position together to find the total number of code words Nell can make:
3 choices for the first letter × 2 choices for the second letter × 2 choices for the third letter × 1 choice for the fourth letter × 1 choice for the fifth letter = 12 code words.
Therefore, Nell can make 12 code words with 3 consonants and 2 vowels.