How many lists of length 3 can be made from the letters U, V, W, X, Y, Z if repetitions are allowed? 2. How many lists of length 3 can be made from the letters U, V, W, X, Y, Z if repetitions are not allowed? 3. How many lists of length 3 can be made from the letters U, V, W, X, Y, Z if repetitions are not allowed, and each list has a W or U in the second entry?

Step-by-step explanation:

1. How many lists of length 3 can be made from the letters U, V, W, X, Y, Z if repetitions are allowed?

From the question, there are 6 letters available which are U, V, W, X, Y, and Z. We are told to make a list of length 3 and that repetition are allowed. This will be:

= 6 × 6 × 6

= 216

2. How many lists of length 3 can be made from the letters U, V, W, X, Y, Z if repetitions are not allowed?

Since repetitions are not allowed and we want to make a list of length 3, at first there will be 6 letters, then there'll be 5 letters and lastly 4 letters. This will now be:

= 6 × 5 × 4

= 120

3. When repetitions are not allowed, and each list has a W or U in the second entry, then this will be any alphabet except one in second place which will be 5 multiplied by alphabet except those used in first or secone place multiplied by the two alphabets. This will be:

= 5 × 4 × 2

= 40

true

step-by-step explanation:

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