मराठी

If 20cr = 20cr−10, Then 18cr is Equal to (A) 4896 (B) 816 (C) 1632 (D) Nont of These - Mathematics

Advertisements
Advertisements

प्रश्न

If 20Cr = 20Cr−10, then 18Cr is equal to

पर्याय

  • 4896

  • 816

  • 1632

  •  nont of these

MCQ
Advertisements

उत्तर

816

\[r + r - 10 = 20\] [∵\[{}^n C_x =^n C_y \Rightarrow n = x + y\ \text{or} x = y\]]
\[\Rightarrow 2r - 10 = 20\]
\[ \Rightarrow 2r = 30\]
\[ \Rightarrow r = 15\]
Now,
\[{}^{18} C_r =^{18} C_{15}\]
\[\therefore {}^{18} C_{15} = {}^{18} C_3\]
\[\therefore^{18} C_3 = \frac{18}{3} \times \frac{17}{2} \times 16 = 816\]
shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 17: Combinations - Exercise 17.5 [पृष्ठ २५]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
पाठ 17 Combinations
Exercise 17.5 | Q 1 | पृष्ठ २५

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

If nC8 = nC2, find nC2.


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.


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


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


Prove that

\[\frac{1}{9!} + \frac{1}{10!} + \frac{1}{11!} = \frac{122}{11!}\]

In how many ways can an examinee answer a set of ten true/false type questions?


A team consists of 6 boys and 4 girls and other has 5 boys and 3 girls. How many single matches can be arranged between the two teams when a boy plays against a boy and a girl plays against a girl?


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


How many odd numbers less than 1000 can be formed by using the digits 0, 3, 5, 7 when repetition of digits is not allowed?


How many four digit different numbers, greater than 5000 can be formed with the digits 1, 2, 5, 9, 0 when repetition of digits is not allowed?


If 28C2r : 24C2r − 4 = 225 : 11, find r.


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.


How many different selections of 4 books can be made from 10 different books, if two particular books are never selected?


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 committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of these committees would consist of 1 man and 2 women?


We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can the selection be made?


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.


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?


Find the number of ways in which : (b) an arrangement, of four letters can be made from the letters of the word 'PROPORTION'.


Write \[\sum^m_{r = 0} \ ^{n + r}{}{C}_r\] in the simplified form.


There are 3 letters and 3 directed envelopes. Write the number of ways in which no letter is put in the correct envelope.


There are 12 points in a plane. The number of the straight lines joining any two of them when 3 of them are collinear, is


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


In how many ways can a committee of 5 be made out of 6 men and 4 women containing at least one women?


The value of\[\left( \ ^{7}{}{C}_0 + \ ^{7}{}{C}_1 \right) + \left( \ ^{7}{}{C}_1 + \ ^{7}{}{C}_2 \right) + . . . + \left( \ ^{7}{}{C}_6 + \ ^{7}{}{C}_7 \right)\] is


Among 14 players, 5 are bowlers. In how many ways a team of 11 may be formed with at least 4 bowlers?


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


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 15C4 + 15C5 


Answer the following:

A question paper has 6 questions. How many ways does a student have to answer if he wants to solve at least one question?


If α = mC2, then αCis equal to.


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 ______.


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 from the lot.


If nCr – 1 = 36, nCr = 84 and nCr + 1 = 126, then find rC2.


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?


Given 5 different green dyes, four different blue dyes and three different red dyes, the number of combinations of dyes which can be chosen taking at least one green and one blue dye is ______.


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

Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear is ______.


The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×