Class 12 Permutation and Combination Exercise 1.2 Solutions | Basic Mathematics Sukunda Pustak Bhawan

Find the number of permutations of five different objects taken three at a time.

If three persons enter a bus in which there are ten vacant seats, find in how many ways they can sit.

How many plates of vehicles consisting of 4 different digits can be made out of the integers $\rm 4, 5, 6, 7, 8, 9 \;$? How many of these numbers are divisible by 2?

How many numbers of 4 different digits can be formed from the digits $\rm 2, 3, 4, 5, 6, 7 $ ? How many of these numbers are $ i) $ divisible by 5$\;$ $ ii)$  not divisible by 5. 

How many 5-digit odd numbers can be formed using the digits $\rm 3, 4, 5, 6, 7, 8,$ and $\rm 9 $. If $\rm i)$ repetition of digits is not allowed $\;$ $\rm ii)$ repetition of digits is allowed?

In how many ways can four boys and three girls be seated in a row containing seven seats 

1. if they may sit anywhere
2. if the boys and girls must alternate
3. if all three girls are together
4. if girls are to occupy odd seats

In how many ways can eight people be seated in a row of eight seats so that two particular persons are $\rm a)$ always together $\rm b) $ never together? 

Six different books are arranged on a shelf. Find the number of different ways in which the two particular books are $\rm a) $ always together $\rm b)$ not together. 

In how many ways can four red beads, five white beads, and three blue beads be arranged in a row?

In how many ways can the letters of the following words be arranged?

1. ELEMENT
2. NOTATION
3. MATHEMATICS
4. MISSISSIPPI

How many numbers of 6 digits can be formed with the digits $ 2, 3, 2, 0, 3, 3\;$?

In how many ways can 4 Art students and 4 science students be arranged in a circular table if $\rm a) $ they may sit anywhere $\rm b) $ they sit alternately? 

In how many ways can eight people be seated at a round table if two people insist on sitting next to each other?

In how many ways can seven different coloured beads be made into a bracelet?

In how many ways can 4 letters be posted in six-letter boxes?

How many even numbers of 3 digits can be formed when repetition of digits is allowed?

In how many ways can 3 prizes be distributed among 4 students so that each student may receive any number of prizes?

In how many ways can the letters of the word “MONDAY” be arranged? How many of these arrangements do not begin with M? How many begin with M and do not end with Y?

Show that the number of ways in which the letters of the word “COLLEGE” can be arranged so that the two E's always come together is 360.

Show that the number of ways in which the letters of the word “ARRANGE” can be arranged so that no two R's come together is 900.

In how many ways can the letters of the word ‘COMPUTER’ be arranged so that 

1. all the vowels are always together?
2. the vowels may occupy only odd positions?
3. the relative positions of vowels and consonants are not changed?

Find the number of arrangements of the letters of the word “LAPTOP” so that 

1. the vowels may never be separated;
2. all the consonants may not be together;
3. they always begin with L and end with T
4. They do not begin with L but always end with T.

How many different words can be formed with all the letters of the word “INTERNET” if

1. each word is, to begin with vowel?
2. each word is to end with consonant?