मराठी

If Nc4 = Nc6, Find 12cn.

Advertisements
Advertisements

प्रश्न

If nC4 = nC6, find 12Cn.

Advertisements

उत्तर

We have,
\[{}^n C_4 = {}^n C_6\]

\[\Rightarrow n = 6 + 4 = 10\]  [∵ \[{}^n C_x = {}^n C_y \Rightarrow x = y\]]  or, \[n = x + y\]
Now, \[{}^{12} C_{10} = {}^{12} C_2\][∵ \[{}^n C_r = {}^n C_{n - r}\]]
\[\Rightarrow^{12} C_{10} =^{12} C_2 = \frac{12}{2} \times \frac{11}{1} \times^{10} C_0\] [∵ \[{}^n C_r = \frac{n}{r} {}^{n - 1} C_{r - 1}\]]
\[\Rightarrow {}^{12} C_{10} = 66\]  [∵\[{}^n C_0 = 1\]]
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 3 | पृष्ठ ८

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

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


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, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?


How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated?


Compute:

\[\frac{11! - 10!}{9!}\]

Prove that

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

There are 6 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next three have 2 each?


Given 7 flags of different colours, how many different signals can be generated if a signal requires the use of two flags, one below the other?


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 different numbers of six digits can be formed from the digits 3, 1, 7, 0, 9, 5 when repetition of digits is not allowed?


If n +2C8 : n − 2P4 = 57 : 16, find n.


If 16Cr = 16Cr + 2, find rC4.


From a group of 15 cricket players, a team of 11 players is to be chosen. In how many ways can this be done?


How many different boat parties of 8, consisting of 5 boys and 3 girls, can be made from 25 boys and 10 girls?


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 professor is included.


From a class of 12 boys and 10 girls, 10 students are to be chosen for a competition; at least including 4 boys and 4 girls. The 2 girls who won the prizes last year should be included. In how many ways can the selection be made?


From 4 officers and 8 jawans in how many ways can 6 be chosen. to include at least one officer?


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


Find the number of (i) diagonals


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: atmost 3 girls?


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


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


If C0 + C1 + C2 + ... + Cn = 256, then 2nC2 is equal to


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


If n + 1C3 = 2 · nC2 , then n =


Find n if `""^6"P"_2 = "n" ""^6"C"_2`


Find the value of 15C4 


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?


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


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 ______.


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 nC12 = nC8, then n is equal to ______.


Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. The total number of persons in the room is ______.


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 ______.


In a football championship, 153 matches were played, Every two teams played one match with each other. The number of teams, participating in the championship is ______.


There are 12 points in a plane of which 5 points are collinear, then the number of lines obtained by joining these points in pairs is 12C25C2.


There are (n + 1) white and (n + 1) black balls each set numbered 1 to (n + 1). The number of ways in which the balls can be arranged in row so that the adjacent balls are of different colours is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×