मराठी

If nC8 = nC2, find nC2.

Advertisements
Advertisements

प्रश्न

If nC8 = nC2, find nC2.

बेरीज
Advertisements

उत्तर

nC8 = nC2 = nCn - 2

nC8 = nCn - 2

8 = n - 2

∴ n = 10

nC2 = 10C2 = `(10!)/(2!(10 - 2)!) = (10!)/(2!8!)` = `(10 xx 9 xx 8!)/(2 xx 1 xx 8!) = 45.`

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 6: Permutations and Combinations - EXERCISE 6.4 [पृष्ठ ११९]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 11
पाठ 6 Permutations and Combinations
EXERCISE 6.4 | Q 1. | पृष्ठ ११९

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?


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?


Compute: 

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


Prove that

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

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?


A mint prepares metallic calendars specifying months, dates and days in the form of monthly sheets (one plate for each month). How many types of calendars should it prepare to serve for all the possibilities in future years?


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


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 three-digit odd numbers are there?


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 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?


A number lock on a suitcase has 3 wheels each labelled with ten digits 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible? Also, find the number of unsuccessful attempts to open the lock.


Evaluate the following:

14C3


Evaluate the following:

12C10


If nC12 = nC5, find the value of n.


If 18Cx = 18Cx + 2, find x.


Find the number of (i) diagonals


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?


5C1 + 5C2 5C3 + 5C4 +5C5 is equal to


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


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


Find n if `""^(2"n")"C"_3: ""^"n""C"_2` = 52:3


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.


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?


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?


In how many ways a committee consisting of 3 men and 2 women, can be chosen from 7 men and 5 women?


All the letters of the word ‘EAMCOT’ are arranged in different possible ways. The number of such arrangements in which no two vowels are adjacent to each other is ______.


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 selections 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 from the lot.


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


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 ______.


The total number of ways in which six ‘+’ and four ‘–’ signs can be arranged in a line such that no two signs ‘–’ occur together is ______.


Eighteen guests are to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on other side of the table. The number of ways in which the seating arrangements can be made is `(11!)/(5!6!) (9!)(9!)`.


To fill 12 vacancies there are 25 candidates of which 5 are from scheduled castes. If 3 of the vacancies are reserved for scheduled caste candidates while the rest are open to all, the number of ways in which the selection can be made is 5C3 × 20C9.


A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed is ______.


The number of numbers between 2,000 and 5,000 that can be formed with the digits 0, 1, 2, 3, 4, (repetition of digits is not allowed) and are multiple of 3 is?


From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then, the number of such arrangements is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×