मराठी

If 15cr : 15cr − 1 = 11 : 5, Find R.

Advertisements
Advertisements

प्रश्न

If 15Cr : 15Cr − 1 = 11 : 5, find r.

Advertisements

उत्तर

Given:
 15Cr : 15Cr − 1 = 11 : 5
We have,

\[\frac{{}^{15} C_r}{{}^{15} C_{r - 1}} = \frac{11}{5}\]

\[\Rightarrow \frac{15 - r + 1}{r} = \frac{11}{5}\]
\[\frac{{}^n C_r}{{}^n C_{r - 1}} = \frac{n - r + 1}{r}\]

\[\Rightarrow 75 - 5r + 5 = 11r\]
\[ \Rightarrow 16r = 80\]
\[ \Rightarrow r = 5\]

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 17: Combinations - Exercise 17.1 [पृष्ठ ८]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
पाठ 17 Combinations
Exercise 17.1 | Q 9 | पृष्ठ ८

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

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


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?


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?


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


How many different five-digit number licence plates can be made if

the first-digit cannot be zero, but the repetition of digits is allowed?


How many different numbers of six digits each can be formed from the digits 4, 5, 6, 7, 8, 9 when repetition of digits is not allowed?


Evaluate the following:

14C3


Evaluate the following:

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

 


If nC10 = nC12, find 23Cn.


If nC4 , nC5 and nC6 are in A.P., then find n.


In how many ways can a student choose 5 courses out of 9 courses if 2 courses are compulsory for every student?


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.


In how many ways can a committee of 5 persons be formed out of 6 men and 4 women when at least one woman has to be necessarily selected?


In a village, there are 87 families of which 52 families have at most 2 children. In a rural development programme, 20 families are to be helped chosen for assistance, of which at least 18 families must have at most 2 children. In how many ways can the choice be made?


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


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?


Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (ii) triangles can be formed by joining them?


If 20Cr = 20Cr + 4 , then rC3 is equal to


If 20Cr + 1 = 20Cr − 1 , then r is equal to


If nC12 = nC8 , then n =


Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to


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


There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two of them is


There are 13 players of cricket, out of which 4 are bowlers. In how many ways a team of eleven be selected from them so as to include at least two bowlers?


The number of ways in which a host lady can invite for a party of 8 out of 12 people of whom two do not want to attend the party together is


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


There are 20 straight lines in a plane so that no two lines are parallel and no three lines are concurrent. Determine the number of points of intersection.


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?


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?


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


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 they can be of any colour


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 at least three girls.


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 ______.


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


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

If number of arrangements of letters of the word "DHARAMSHALA" taken all at a time so that no two alike letters appear together is (4a.5b.6c.7d), (where a, b, c, d ∈ N), then a + b + c + d is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×