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This problem involves lists made from the letters T, H, E, O, R, Y, with repetition allowed. (a) How many 4-letter lists are there that don’t begin with T, or don’t end in Y? (b) How many 4-letter lists are there in which the sequence of letters T, H, E appears consecutively (in that order)? (c) How many 6-letter lists are there in which the sequence of letters T, H, E appears consecutively (in that order)?

Respuesta :

From the sequence given, the 4-letter lists are there that don’t begin with T, or don’t end in Y will be 900.

Computing the sequence.

The number of 4-letter lists are there that don’t begin with T, or don’t end in Y will be:

= 5 × 6 × 6 × 5

= 900

The number of 4-letter lists that are there in which the sequence of letters T, H, E appears consecutively will be:

= 6 × 3!

= 6 × 3 × 2

= 36

The number of 6-letter lists that are there in which the sequence of letters T, H, E appears consecutively will be:

= 6⁴ = 1296 ways

Learn more about sequence on:

https://brainly.com/question/6561461

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