Discussion questions · Section 1 of 3

Given the digits 1, 2, 3, 4, 6 and 8, and using each digit at most once, determine how many numbers can be formed if the number has to be

(i) less than 100,

(ii) between 100 and 1000,

(iii) between 1000 and 10000.

A girl wishes to phone a friend but cannot remember the exact number. She knows that it is a five-digit number, that it is even, and that it consists of the digits 2, 3, 4, 5 and 6 in some order. Using this information, find the largest number of different wrong telephone numbers she could try.

Find the number of ways in which 6 people may be divided into groups of

(i) 1, 2 and 3,

(ii) 2, 2 and 2,

(iii) 3, 1, 1 and 1.

A four-letter word can be formed from any of the 26 letters in the alphabet. Determine the number of such words with

(i) repetitions of the letters allowed,

(ii) different letters and containing exactly one vowel,

(iii) repetitions allowed and containing at least one vowel.

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.