Permutations and Combinations

In how many ways can the letters of the word PERMUTATIONS be arranged if
the
(i) words start with P and with S
(ii) vowels are all together
(iii) There are always 4 letters between P and S?

A committee of 5 is to be formed out of 6 gents and 4 Ladies. In how many
ways this can be done, when
(i) at least two ladies are included?
(ii) at most two ladies are included?

Find the number of 3 digit even number that can be made using the digits 1, 2,
3, 4, 5, 6, 7, if no digit is repeated?

Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls
and 5 blue balls if each selection consists of 3 balls of each colour.

From a class of 25 students 10 are to be chosen for an excursion Party. There
are 3 students who decide that either all of them will join or none of them will
join. In how many ways can excursion party be chosen?

How many words with or without meaning can be formed using all the letters
of the word ‘EQUATION’ at a time so that vowels and consonants occur
together

Convert into factorial 2.4.6.8.10.12

How many 3 digit numbers can be formed by using the digits 1 to 9 if no. digit
is repeated

How many four letter words can be formed using the letters of the letters of
the word ‘FAILURE’ so that
(i) F is included in each word
(ii) F is excluded in each word.

In how many ways can final eleven be selected from 15 cricket players’ if
(i) there is no restriction
(ii) one of then must be included
(iii) cone of them, who is in bad form, must always be excluded
(iv) Two of then being leg spinners, one and only one leg spinner must be
included?

How many 4 letter words with or without meaning, can be formed out of the
letters of the word ‘LOGARITHMS’, if repetition of letters is not allowed?

How many numbers greater than 56000 and farmed by using the digits
4,5,6,7,8, no digit being repeated in any number?

Determine the number of ways of choosing 5 cards out of Adele of 52 cards
which include exactly one ace.

Convert the following products into factorials 5´6´7´8´9

A committee of 7 has to be farmed from 9 boys and 4 girls in how many ways
can this be done when the committee consists of
(i) Exactly 3 girls? (ii) Attest 3 girls? (iii) Almost 3 girls?

How many 4 letter code can be formed using the first 10 letters of the English
alphabet if no letter can be repeated?

Find the number of permutations of the letters of the word ALLAHABAD.

In how many ways can 4 red, 3 yellow and 2 green discs be arranged in a row
if the discs of the same colors are in distinguishable?

In how many of the distinct permutations of the letters in MISSISSIPPI do the
four I’s not come together?

The English alphabet has 5 vowels and 21 consonants. How many words with
two different vowels and 2 different consonants can be flamed from the
alphabet?

How many words, with or with not meaning each of 2 vowels and 3
consonants can be flamed from the letter of the word DAUGHTER?

What is the number of ways of choosing 4 cards from a pack of 52 playing
cards? In how many of there
(i) Four cards one of the same suit
(ii) Four cards belong to four different suits
(iii) Are face cards.
(iv) Two are red cards & two are black cards.
(v) Cards are of the same colour?

In how many ways can the letters of the word ASSA SS IN ATION be arranged
so that all the S’s are together?

How many numbers greater than 1000000 can be formed by using the digits
1,2,0,2,4,2,4?

In how many ways can one select a cricket team of eleven from 17 players in
which only 5 players can bowl if each cricket team of 11 must include exactly
4 bowlers?

Find the number of arrangements of the letters of the word INDEPENDENCE.
In how many of these arrangements
(i) do the words start with P
(ii) do all the vowels always occur together

In how many ways of selecting 9 balls from 6 red balls, 5 white balls and 5
blue balls if each selection consists of 3 balls of each colours.

A coin is tossed 3 times and the outcomes are recorded. How many possible
out comes are there?

Find the number of words with or without meaning which can be made using
all the letters of the word. AGAIN. If these words are writer as in a dictionary,
what will be the 50th word?

A group consists of 4 girls and 7 boys. In how many ways can a team of 5
members be selected if the team has :

(i) no girl? (ii) at least one boy and one girl? (iii) at least 3 girls?

How many words, with or without meaning, each of 3 vowels and 2
consonants can be formed from the letters of the word INVOLUTE

In how many ways can 5 girls and 3 boys be seated in a row so that no two
boys are together?

A bag contains 5 black and 6 red balls determine the number of ways in which
2 black and 3 red balls can be selected.

How many words, with or without meaning can be made from the letters of
the word MONDAY. Assuming that no. letter is repeated, it
(i) 4 letters are used at a time
(ii) All letters are used but first letter is a vowel?

How many 4 letter code can be formed using the first 10 letter of the English
alphabet, if no letter can be repeated?

Given 5 flags of different colours here many different signals can be generated
if each signal requires the use of 2 flags. One below the other

The value of 0!

Evaluate 4! - 3!

Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other?

A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?

How many 5-digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once?

How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?

How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?

How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that

(i) repetition of the digits is allowed?

(ii) repetition of the digits is not allowed?