Practice section 4 of 10

(a) Find the number of different arrangements of the nine letters in CELEBRATE in which A and T are next to each other.

(b) Find the number of 3-letter codewords that can be formed from the letters of CELEBRATE.

How many numbers between 3000 and 5000 can be formed using only the digits 1, 2, 3, 4 and 5 if (i) no digit is repeated, (ii) the digits can be repeated, (iii) no repetition is allowed and the numbers are even?

In how many ways can 3 men and 3 women be arranged in a row so that (i) the women are always together, (ii) the men and women occupy alternate places, (iii) the two particular women are always separated by two men?

There are 5 different rides in a fun fair. How many different combinations the child can make if the child has to take at least one ride?

Find the number of ways to arrange the six letters of the word PETALS when (i) there is no restriction, (ii) P is the first letter and E is the last letter, (iii) P and E are together, (iv) P and E are separated.

In how many ways can 4 boys and 4 girls be seated at a round table if (i) there is no restriction, (ii) the boys and the girls must be separated, (iii) one particular girl must be seated between 2 particular boys?