Advertisements
Advertisements
प्रश्न
15C8 + 15C9 – 15C6 – 15C7 = ______.
Advertisements
उत्तर
15C8 + 15C9 – 15C6 – 15C7 = 0.
Explanation:
15C8 + 15C9 – 15C6 – 15C7 = 15C15–8 + 15C15–9 – 15C6 – 15C7 ......[∵ nCr = nCn–r]
= 15C7 + 15C6 – 15C6 – 15C7
= 0
Hence, the value of the filler is 0.
APPEARS IN
संबंधित प्रश्न
Determine n if `""^(2n)C_3 : ""^nC_3 = 12 : 1`
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
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 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?
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?
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?
In a class there are 27 boys and 14 girls. The teacher wants to select 1 boy and 1 girl to represent the class in a function. In how many ways can the teacher make this selection?
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?
A team consists of 6 boys and 4 girls and other has 5 boys and 3 girls. How many single matches can be arranged between the two teams when a boy plays against a boy and a girl plays against a girl?
Twelve students complete in a race. In how many ways first three prizes be given?
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:
n + 1Cn
If nC4 = nC6, find 12Cn.
If 28C2r : 24C2r − 4 = 225 : 11, find r.
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 student is included.
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.
In how many ways can one select a cricket team of eleven from 17 players in which only 5 persons can bowl if each cricket team of 11 must include exactly 4 bowlers?
Find the number of ways in which : (b) an arrangement, of four letters can be made from the letters of the word 'PROPORTION'.
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?
If nC12 = nC8 , then n =
In how many ways can a committee of 5 be made out of 6 men and 4 women containing at least one women?
Find n if `""^(2"n")"C"_3: ""^"n""C"_2` = 52:3
Find n and r if `""^"n""P"_"r"` = 720 and `""^"n""C"_("n" - "r")` = 120
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.
In how many ways can the letters of the word 'IMAGE' be arranged so that the vowels should always occupy odd places?
A boy has 3 library tickets and 8 books of his interest in the library. Of these 8, he does not want to borrow Mathematics Part II, unless Mathematics Part I is also borrowed. In how many ways can he choose the three books to be borrowed?
A box contains two white, three black and four red balls. In how many ways can three balls be drawn from the box, if atleast one black ball is to be included in the draw
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to ______.
The number of ways in which a team of eleven players can be selected from 22 players always including 2 of them and excluding 4 of them 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 12C2 – 5C2.
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!)`.
There are 12 persons seated in a line. Number of ways in which 3 persons can be selected such that atleast two of them are consecutive, 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 ______.
Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear is ______.
