SOLUTION: Given the word BASKETBALL, How many permutations begin with the letter K? And How many permutations have the 2 L's together?

This is the same as the number of distinguishable arrangements of
"BASETBALL" (with no "K"), because we can insert a "K" in front of
each distinguishable arrangement of "BASETBALL" and have a 
distinguishable arrangement of "BASKETBALL beginning with "K".
"BASETBALL" has 9 letters, with 2 indistinguishable A's, 2 
indistinguishable B's, and 2 indistiguishable L's.  So there are 
 = 45360 distinguishable arrangements of "BASETBALL"
that we can insert a "K" in front of to make a distinguishable 
arrangement of "BASKETBALL" which begins with "K".

Answer:  = 45360

This is the same as the number of distinguishable arrangements of
"BASKETBAL" (with just 1 "L"), because we can insert another "L" beside
each "L" in each distinguishable arrangement of "BASKETBAL", and have
a distinguishable arrangement of "BASKETBALL" with 2 "L"'s together. 
"BASKETBAL" has 9 letters, with 2 indistinguishable A's and 2 
indistinguishable B's. So there are  = 90720 
distinguishable arrangements of "BASKETBAL" into which we can insert
another L beside each "L" to make a distinguishable arrangement of 
"BASKETBALL" with the two "L"'s together.

Answer:  = 90720

Edwin