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Find the no. of words can be formed from the word “SUCCESSFUL’?
In ‘SUCCESSFUL’ there are 2 no. of C, 2 no. of S, 2 no. of U and there are total of 10 letters.
Total no. of words
In how many different ways can the letter of the word ‘ELEPHANT’ be arranged so that vowels always occur together?
There are 8 letters in the word ‘ELEPHANT’ & 3 vowels E, E, A.
The vowels arranged themselves in ways.
We can take all the vowels a single letter.
Since we have 5+1=6 no. of letters.
There are 4 bananas, 7 apples & 6 mangoes in a fruit baskets. In how many ways can a person make a selection of fruits from the basket?
There are 4 bananas, 7 apples, 6 mangoes.
We make take 0 banana, 1 banana, 2 banana, 3 banana, 4 banana respectivaly for other fruits also.
Hence the total ways to selectings bananas, apples & mangoes is
ways.
Since we not conclude 0 no. of each fruits hence we subtract 1 ways.
Required no.of ways =2801=279
There are 15 points in a plane out of which 6 are collinear. Find the no. of lines that can be formed from 15 points.
From 15 points no. of lines formed
6 points are collinear, no. of lines formed by these
Total lines
In how many ways 4 Indians, 5 Africans & 7 Japanese be seated in a row so that all person of same nationality sit together?
4 Indians seated in 4! ways.
5 Africans seated in 5! ways.
7 Japanese seated in 7! ways.
All three nationality seated in 3! ways.
Total no.of ways =(4!)(5!)(7!)(3!)
In how many ways 5 americans & 5 Indians be seated along a circluar table, so that they are seated in alternative position?
Indian are seated in 5! ways.
Americans are seated in (51)!=4! ways.
Total no.of ways=(4!)(5!)
4 matches are to be played in a chess tournament. In how many ways can result be decided?
Every chess match can have 3 result i.e. win, loss or draw.
So no.of ways
A box cantain 20 balls. In how many ways can 8 balls be selected if each ball can be repeated any number of times?
Hence n=20, r=8
Required no. of ways
There are 11 Players in a cricket squad which is to be sent to Australian tour i.e. The total no.of members are 15. If 2 particuar member is always included. How manys ways the players could selected in them?
Total no.of players=15
2 particular players are always included.
A squad contain 11 players.
Hence (152=13) players will be take part and (112=9) player are to be chosen.
No. of ways
A box contain 12 black balls, 7 red balls and 6 blue balls. In how many ways can one or more balls be selected?
There are 3 kind of balls.
Required no. of ways=(12+1)(7+1)(6+1)1
=7281=727
There are 12 copies of Mathematics, 7 copies Of Engineering, 3 different books on medicine & 2 different books on Economics. Find the no. of ways in which one on more than one book can be selected?
12 copies of Mathematics, 7 copies of Engineering, 3 different books from medicines & 2 different books of Economics.
If there are 5 different books.
Total no. of ways
There are 10 different books & 20 copies of each book in a library. In how many ways can one or more than one book be selected?
There are 10 different books.
Each book has 200 copies & all the copipes of each particular book can be considered as identical.
Total no. of ways
In how many ways can 4 different balls be distruibuted among 5 different boxes when any box can have any no. of balls?
Hence n=5, k=4
Required no. of ways
In how many ways can 3 different balls be distruibuted among 2 different boxes when any box can have any no. of balls?
Hence n=2, k=3
required no. of ways
In how many ways can 5 distinguishable balls put into 8 disinguishable boxes if no box can contain more than one ball?
Hence n=8, k=5
Required no. of ways
Find the value of m where \({}^8{P_3} = {}^8{C_{3 \times m}}\)
m=3!