Combination of r Things from n Things When All Are Not Different

Q.

From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?

Q. 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.

Q.

How many ways we can get a sum of atmost 17 by throwing six distinct dies.

1. 9604

2. 3493

3. 1914

4. 7756

Q.

How many even numbers are there in the following sequence of numbers, each of which, is followed by an odd number as well as preceded by an even number?

$86768932753422355228119$

Q. 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?

Q. The number of ways of selecting one or more letters from the letters AAAA BBB CDE is

1. 160
2. 159
3. 144
4. 158

Q. 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?

Q.

The number of arrangements of the letters of the word ‘NAVA NAVA LAVANYAM’ which begin with N and end with M is :

1. 

2. 

3. 

4. 

Q. Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.

Q. 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.

Q. 1.IfnC, -"C2, find nC..

Q. In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II , containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?

Q. 2.Determine n if() 2C3 C3 12: 1) 2C3 C11:1

Q. Words are formed using all letters of the word 'JEEADVANCED'.
Let $a$ denotes the number of words in which all the vowels are together.
Let $b$ denotes the number of words in which vowels as well as consonants are separated.
Let $c$ denotes the number of words which begin and end with vowels.

1. $c>a>b$
2. $c>b>a$
3. $a+b+c=460\times 6!$
4. $a+c=91b$

Q. In a polygon no three diagonals are concurrent. If the total number of points of intersection of diagonals interior to the polygon be 70 then the number of diagonals of the polygon is

1. 28
2. 20
3. 8
4. 36

Q. In a polygon no three diagonals are concurrent. If the total number of points of intersection of diagonals interior to the polygon be 70 then the number of diagonals of the polygon is

1. 20
2. 28
3. 8
4. 36

Q. The number of ways in which a committee of 3 women and 4 men be chosen from 8 women and 7 men. If Mr. X refuses to serve on the committee if Mr Y is a member of the committee is

1. 420
2. 840
3. 1540
4. 1400

Q. In a shop there are five types of ice creams available. A child buys six ice creams.
Statement 1: The number of different ways the child can buy the six ice-creams is
${}^{10}{C}_5$.
Statement 2: The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A's and 4 B's in a row.

1. Statement 1 is false, statement 2 is true.
2. Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1.
3. Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1.
4. Statement 1 is true, statement 2 is false.

Q. Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.

Q. The number of four letter words that can be formed using the letters of the word $BARRACK$ is

1. $120$
2. $270$
3. $264$
4. $144$

Q. Number of ways of selecting $6$ shoes, out of $6$ pair of shoes, having exactly two pairs is

1. $1440$
2. $240$
3. $720$
4. $360$

Q. The total number of $4$ letter words that can be formed from the string $"AABBBBCC"$ is

1. $56$
2. $68$
3. $63$
4. $48$

Q. A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: (i) exactly 3 girls? (ii) atleast 3 girls? (iii) atmost 3 girls?

Q. 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?

Q. How many chords can be drawn through 21 points on a circle?

Q. The number of ways of selecting one or more letters from the letters AAAA BBB CDE is

1. 160
2. 159
3. 158
4. 144

Q. The number of ways of choosing a committee of two women and three men from five women and six men, if Mr. A refuses to serve on the committee if Mr. B is a member and Mr. B can only serve, if Miss C is the member of the committee is

1. $84$
2. None of these
3. $124$
4. $60$

Q. In a shop there are five types of ice creams available. A child buys six ice creams.
Statement 1: The number of different ways the child can buy the six ice-creams is
${}^{10}{C}_5$.
Statement 2: The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A's and 4 B's in a row.

1. Statement 1 is false, statement 2 is true.
2. Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1.
3. Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1.
4. Statement 1 is true, statement 2 is false.