Question

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)?

Answer 1

Answer:

Step-by-step explanation:

a.Consider A- 4 letter list don't begin with T & B-4 letter list don't end with Y

$\left | A \right |$=5×6×6×6=1080

$\left | B \right |$=6×6×6×5=1080

$\left | A\bigcap B \right |$=5×6×6×5=900

$\left | A\bigcup B \right |$=1080+1080-900=1260

b.$\left ( 6+6 \right )$=12

c.$\left ( 6*6*6\right )+\left ( 6*6*6 \right )$=216+216=432