English

Compute: (I) 30 ! 28 !

Advertisements
Advertisements

Question

Compute: 

(i)\[\frac{30!}{28!}\]

Advertisements

Solution

\[ \frac{30!}{28!} = \frac{30 \times 29 \times 28!}{28!} \left[ \because n! = n(n - 1)! \right]\]
\[ = 30 \times 29\]
\[ = 870\]

shaalaa.com
  Is there an error in this question or solution?
Chapter 16: Permutations - Exercise 16.1 [Page 4]

APPEARS IN

R.D. Sharma Mathematics [English] Class 11
Chapter 16 Permutations
Exercise 16.1 | Q 1.1 | Page 4

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

If nC8 = nC2, find nC2.


Determine n if  `""^(2n)C_3 : ""^nC_3 = 12 : 1`


If the different permutations of all the letter of the word EXAMINATION are listed as in a dictionary, how many words are there in this list before the first word starting with E?


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


It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?


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 the excursion party be chosen?


Compute:

 L.C.M. (6!, 7!, 8!)


There are four parcels and five post-offices. In how many different ways can the parcels be sent by registered post?


Twelve students complete in a race. In how many ways first three prizes be given?


How many A.P.'s with 10 terms are there whose first term is in the set {1, 2, 3} and whose common difference is in the set {1, 2, 3, 4, 5}?


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?


In how many ways can six persons be seated in a row?


Evaluate the following:

\[\sum^5_{r = 1} {}^5 C_r\]

 


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 included.


In an examination, a student has to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make the choice.


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 (ii) triangles


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?


In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?


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?


If 15C3r = 15Cr + 3 , then r is equal to


Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?


The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is


Five students are selected from 11. How many ways can these students be selected if two specified students are not selected?


Find the value of 20C1619C16 


If α = mC2, then αCis equal to.


A student has to answer 10 questions, choosing atleast 4 from each of Parts A and B. If there are 6 questions in Part A and 7 in Part B, in how many ways can the student choose 10 questions?


There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated.


If 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, in how many points will they intersect each other?


A convex polygon has 44 diagonals. Find the number of its sides.


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 include 2 particular players?


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 no girls


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 ______.


The number of ways in which we can choose a committee from four men and six women so that the committee includes at least two men and exactly twice as many women as men is ______.


15C8 + 15C915C615C7 = ______.


If some or all of n objects are taken at a time, the number of combinations is 2n – 1.


Number of selections of at least one letter from the letters of MATHEMATICS, is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×