Practice By Tag: Reordering the Letters of a Word

Question: 2019 Fall Final - 8

1 . A string that is obtained by rearranging the letters of the word BOOGER is called awesome, if the string does not contain the substring OO. Thus, GEOROB is awesome, whereas GREOOB is not awesome. What is the number of awesome strings?

(a)

$(6 \cdot {5 \choose 2} \cdot 3) - 5!$

(b)

$(6 \cdot {5 \choose 2} \cdot 3 \cdot 2) - 5!$

(c)

$6! - 5!$

(d)

$6 \cdot {5 \choose 2} \cdot 3 \cdot 2$