Advertisements
Advertisements
प्रश्न
Compute:
उत्तर
\[\frac{11! - 10!}{9!} = \frac{11 \times 10 \times 9! - 10 \times 9!}{9!} \left[ \because n! = n(n - 1)! \right]\]
\[ = \frac{9!(110 - 10)}{9!}\]
\[ = 100\]
APPEARS IN
संबंधित प्रश्न
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
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?
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.
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?
Compute:
(i)\[\frac{30!}{28!}\]
A person wants to buy one fountain pen, one ball pen and one pencil from a stationery shop. If there are 10 fountain pen varieties, 12 ball pen varieties and 5 pencil varieties, in how many ways can he select these articles?
How many different five-digit number licence plates can be made if
first digit cannot be zero and the repetition of digits is not allowed,
How many four-digit numbers can be formed with the digits 3, 5, 7, 8, 9 which are greater than 7000, if repetition of digits is not allowed?
Evaluate the following:
12C10
Evaluate the following:
n + 1Cn
If nC12 = nC5, find the value of n.
If 16Cr = 16Cr + 2, find rC4.
There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees:
a particular student is excluded.
A candidate is required to answer 7 questions out of 12 questions which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. In how many ways can he choose the 7 questions?
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?
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.
In how many ways can one select a cricket team of eleven from 17 players in which only 5 persons can bowl if each cricket team of 11 must include exactly 4 bowlers?
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: at least 3 girls?
How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?
If 20Cr = 20Cr−10, then 18Cr is equal to
If 20Cr + 1 = 20Cr − 1 , then r is equal to
If nC12 = nC8 , then n =
A lady gives a dinner party for six guests. The number of ways in which they may be selected from among ten friends if two of the friends will not attend the party together is
Find n if `""^(2"n")"C"_3: ""^"n""C"_2` = 52:3
Find the number of ways of dividing 20 objects in three groups of sizes 8, 7, and 5.
In how many ways can the letters of the word 'IMAGE' be arranged so that the vowels should always occupy odd places?
A boy has 3 library tickets and 8 books of his interest in the library. Of these 8, he does not want to borrow Mathematics Part II, unless Mathematics Part I is also borrowed. In how many ways can he choose the three books to be borrowed?
The straight lines l1, l2 and l3 are parallel and lie in the same plane. A total numbers of m points are taken on l1; n points on l2, k points on l3. The maximum number of triangles formed with vertices at these points are ______.
How many committee of five persons with a chairperson can be selected from 12 persons.
A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if two must be white and two red
In how many ways can a football team of 11 players be selected from 16 players? How many of them will exclude 2 particular players?
If nC12 = nC8, then n is equal to ______.
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is ______.
The number of ways in which a team of eleven players can be selected from 22 players always including 2 of them and excluding 4 of them is ______.
A committee of 6 is to be chosen from 10 men and 7 women so as to contain atleast 3 men and 2 women. In how many different ways can this be done if two particular women refuse to serve on the same committee ______.
There are 3 books on Mathematics, 4 on Physics and 5 on English. How many different collections can be made such that each collection consists of:
C1 | C2 |
(a) One book of each subject; | (i) 3968 |
(b) At least one book of each subject: | (ii) 60 |
(c) At least one book of English: | (iii) 3255 |
There are 10 professors and 20 lecturers out of whom a committee of 2 professors and 3 lecturer is to be formed. Find:
C1 | C2 |
(a) In how many ways committee: can be formed | (i) 10C2 × 19C3 |
(b) In how many ways a particular: professor is included | (ii) 10C2 × 19C2 |
(c) In how many ways a particular: lecturer is included | (iii) 9C1 × 20C3 |
(d) In how many ways a particular: lecturer is excluded | (iv) 10C2 × 20C3 |
There are 12 persons seated in a line. Number of ways in which 3 persons can be selected such that atleast two of them are consecutive, is ______.
Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear is ______.