Advertisements
Advertisements
प्रश्न
If nC8 = nC2, find nC2.
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.`
APPEARS IN
संबंधित प्रश्न
How many chords can be drawn through 21 points on a circle?
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?
Compute:
L.C.M. (6!, 7!, 8!)
Prove that
Since the number has to be greater than 8000, the thousand's place can be filled by only two digits, i.e. 8 and 9.
Now, the hundred's place can be filled with the remaining 4 digits as the repetition of the digits is not allowed.
The ten's place can be filled with the remaining 3 digits.
The unit's place can be filled with the remaining 2 digits.
Total numbers that can be formed = `2xx4xx3xx2=48`
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?
Evaluate the following:
If 15C3r = 15Cr + 3, find r.
If nC4 , nC5 and nC6 are in A.P., then find n.
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?
How many different products can be obtained by multiplying two or more of the numbers 3, 5, 7, 11 (without repetition)?
How many different selections of 4 books can be made from 10 different books, if
there is no restriction;
From 4 officers and 8 jawans in how many ways can 6 be chosen. to include at least one officer?
A sports team of 11 students is to be constituted, choosing at least 5 from class XI and at least 5 from class XII. If there are 20 students in each of these classes, in how many ways can the teams be constituted?
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?
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.
Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination.
How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?
A business man hosts a dinner to 21 guests. He is having 2 round tables which can accommodate 15 and 6 persons each. In how many ways can he arrange the guests?
Find the number of combinations and permutations of 4 letters taken from the word 'EXAMINATION'.
A tea party is arranged for 16 persons along two sides of a long table with 8 chairs on each side. Four persons wish to sit on one particular side and two on the other side. In how many ways can they be seated?
Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?
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?
Given 11 points, of which 5 lie on one circle, other than these 5, no 4 lie on one circle. Then the number of circles that can be drawn so that each contains at least 3 of the given points 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
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
Find n if `""^(2"n")"C"_3: ""^"n""C"_2` = 52:3
Find the value of 15C4
Find the value of 20C16 – 19C16
In how many ways a committee consisting of 3 men and 2 women, can be chosen from 7 men and 5 women?
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 ______.
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 football team of 11 players be selected from 16 players? How many of them will include 2 particular players?
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 ______.
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 ______.
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 ______.

