PERMUTATION COMBINATION-HELP needeed

[elixa]

Q.a wrd is made using 7 letters of the word EXAMPLE. hw many difrnt wrds r possible if the two letters E are NOT next to each other??

Q.A coin is tossed ten times.
(i) how many different sequences of heads and tails are possible?
(ii)how many different sequences containing six heads and four tails are possible?

Q.Calculate the number of ways in which 3 girls and 4 boys can be seated on a row of seven chairs if each arrangement is to be symmetrical?

PLZZ EXPLAIN THESE ALL IN DETAIL...HAVE NO TYM...........

 

[hina]

since the 2 E's that are to be together are identical letters,
they are just equivalent to one E
and the word can now be considered as one of 6 different letters

# of words possible
= 6P6 = 6!
= 720

lets hope some1 answers the rest soon!!