1 .
A string that is obtained by rearranging the letters of the word
POOPERSCOOPER
is called cool, if each occurrence of E has the letter R to its left or right, and each occurrence of R has the letter E to its left or right. Thus, bothPOOPERSCOOPER
andOPRECSOOOERPP
are cool, whereasEPOOPRSCOOPER
is not cool. What is the number of cool strings?
(a)
${11 \choose 3} \cdot {8 \choose 4} \cdot {4 \choose 2} \cdot {2 \choose 1} \cdot {1 \choose 1}$
(b)
${11 \choose 3} \cdot {8 \choose 4} \cdot {4 \choose 2} \cdot {2 \choose 1} \cdot {1 \choose 1} \cdot 3$
(c)
${11 \choose 3} \cdot {8 \choose 4} \cdot {4 \choose 2} \cdot {2 \choose 1} \cdot {1 \choose 1} \cdot 2$
(d)
${11 \choose 3} \cdot {8 \choose 4} \cdot {4 \choose 2} \cdot {2 \choose 1} \cdot {1 \choose 1} \cdot 4$