Practice section 6 of 10

Find the number of arrangements of the 6 letters in the word ELEVEN in which

(i) there are no restrictions,

(ii) all the 3 letters E are consecutive,

(iii) the first letter is E and the last letter is N,

(iv) the first letter is E or the last letter is N or both.

4 distinct green books, 4 distinct blue books and 2 distinct red books are arranged on a shelf. The green books are always placed together in the same order, but the red books are always separated. Calculate the number of ways in which this can be done.

Naval signals are made by arranging coloured flags in a vertical line and the flags are read from top to bottom. How many different signals can be made from 1 green, 3 red and 2 blue flags if

(i) all 6 of the flags are used,

(ii) at least 5 of them are used?

Three single men, two single women and two families take their places at a round table. Each of the two families consists of two parents and one child. Find the number of possible seating arrangements if

(i) members of the same family are seated together and the two single women are separated,

(ii) the seats are numbered and each child sits between their parents.

A box contains 8 balls, of which 3 are identical (and so are indistinguishable from one another) and the other 5 are different from each other. 3 balls are to be picked out of the box, the order in which they are picked out does not matter. Find the number of different possible selections of 3 balls.

Using the letters of the word CORRELATION, find the number of

(i) arrangements such that the two letters A and T are next to each other,

(ii) 6-letter code words that can be formed.