Q.9 If repetitions are not permitted

(i) How many 3 digit numbers can be formed from the six digits 2, 3, 5, 6, 7 & 9?

(ii) How many of these are less than 400 ?

(iii) How many are even ?

(iv) How many are odd ?

(v) How many are multiples of 5 ?

Q.10 In how many ways can 5 letters be mailed if there are 3 mailboxes available if each letter can be mailed in any mailbox.

Q.11 Every telephone number consists of 7 digits. How many telephone numbers are there which do not include any other digits but 2 , 3 , 5 & 7 ?

Q.12(a) In how many ways can four passengers be accommodate in three railway carriages, if each carriage can accommodate any number of passengers.

(b) In how many ways four persons can be accommodated in 3 different chairs if each person can occupy only one chair.

Q.13 How many of the arrangements of the letter of the word “LOGARITHM” begin with a vowel and end with a consonant?

Q.14 How many four digit numbers are there all whose digits are odd , if repetition of digits is allowed.

Q.15 How many four digit numbers are there which are divisible by 2.

Q.16 In a telephone system four different letter P, R, S, T and the four digits 3, 5, 7, 8 are used. Find the maximum number of “telephone numbers” the system can have if each consists of a letter followed by a four-digit number in which the digit may be repeated.

Q.17 Find the number of 5 lettered palindromes which can be formed using the letters from the English alphabets.

Q.18 Number of ways in which 7 different colours in a rainbow can be arranged if green is always in the middle.

Q.19 Two cards are drawn one at a time & without replacement from a pack of 52 cards. Determine the number of ways in a definite order in which the two cards can be drawn in a definite order.

Q.20 It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?

Q.21 Numbers of words which can be formed using all the letters of the word "AKSHI", if each word begins with vowel or terminates in vowel.

Q.22 A letter lock consists of three rings each marked with 10 different letters. Find the number of ways in which it is possible to make an unsuccessful attempts to open the lock.

Q.23 How many 10 digit numbers can be made with odd digits so that no two consecutive digits are same.

Q.24 If no two books are alike, in how many ways can 2 red, 3 green, and 4 blue books be arranged on a shelf so that all the books of the same colour are together?

Q.25 How many natural numbers are there with the property that they can be expressed as the sum of the cubes of two natural numbers in two different ways.

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