मराठी

Evaluate the Following:14c3 - Mathematics

Advertisements
Advertisements

प्रश्न

Evaluate the following:

14C3

Advertisements

उत्तर

We have,

\[{}^{14} C_3 = \frac{14}{3} \times \frac{13}{2} \times \frac{12}{1} \times^{11} C_0\]  [∵\[{}^n C_r = \frac{n}{r} {}^{n - 1} C_{r - 1}\]
\[\Rightarrow\]\[{}^{14} C_3 = 364\]  [∵ \[{}^n C_0 = 1\]]
shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 17: Combinations - Exercise 17.1 [पृष्ठ ८]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
पाठ 17 Combinations
Exercise 17.1 | Q 1.1 | 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?


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:

(i) exactly 3 girls?

(ii) atleast 3 girls?

(iii) atmost 3 girls?


Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.


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?


There are 5 books on Mathematics and 6 books on Physics in a book shop. In how many ways can a students buy : (i) a Mathematics book and a Physics book (ii) either a Mathematics book or a Physics book?


How many three-digit numbers are there with no digit repeated?


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 3-digit numbers are there, with distinct digits, with each digit odd?


If nC4 = nC6, find 12Cn.


If 18Cx = 18Cx + 2, find x.


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


If 2nC3 : nC2 = 44 : 3, find n.


How many different products can be obtained by multiplying two or more of the numbers 3, 5, 7, 11 (without repetition)?


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?


Determine the number of 5 cards combinations out of a deck of 52 cards if at least one of the 5 cards has to be a king?


Find the number of combinations and permutations of 4 letters taken from the word 'EXAMINATION'.


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


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?


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 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.


Ten students are to be selected for a project from a class of 30 students. There are 4 students who want to be together either in the project or not in the project. Find the number of possible selections.


Find the value of 15C4 


The value of `(""^9"C"_0 + ""^9"C"_1) + (""^9"C"_1 + ""^9"C"_2) + ... + (""^9"C"_8 + ""^9"C"_9)` is ______ 


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?


How many committee of five persons with a chairperson can be selected from 12 persons.


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?


If nC12 = nC8, then n is equal to ______.


The number of triangles that are formed by choosing the vertices from a set of 12 points, seven of which lie on the same line is ______.


The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines 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 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsmen and 1 wicketkeeper, is ______.


All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of such numbers in which the odd digits occupy even places is ______.


The no. of different ways, the letters of the word KUMARI can be placed in the 8 boxes of the given figure so that no row remains empty will be ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×