Advertisements
Advertisements
प्रश्न
Find the value of 20C16 – 19C16
Advertisements
उत्तर
20C16 – 19C16
= 19C16 + 19C15 – 19C16 ...[∵ nCr + nCr–1 = n+1Cr]
= 19C15
= `(19!)/(15!(19 - 15)!)`
= `(19!)/(15!4!)`
= `(19 xx 18 xx 17 xx 16 xx 15!)/(15! xx 4 xx 3 xx 2 xx 1)`
= 19 × 6 × 17 × 2
= 3876
∴ 20C16 – 19C16 = 19C15 = 3876
APPEARS IN
संबंधित प्रश्न
In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?
The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet?
Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.
Prove that
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?
From Goa to Bombay there are two roots; air, and sea. From Bombay to Delhi there are three routes; air, rail and road. From Goa to Delhi via Bombay, how many kinds of routes are there?
A coin is tossed five times and outcomes are recorded. How many possible outcomes are there?
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?
From among the 36 teachers in a college, one principal, one vice-principal and the teacher-incharge are to be appointed. In how many ways can this be done?
How many different five-digit number licence plates can be made if
first digit cannot be zero and the repetition of digits is not allowed,
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 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:
f 24Cx = 24C2x + 3, find x.
If 18Cx = 18Cx + 2, find x.
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.
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.
How many different selections of 4 books can be made from 10 different books, if two particular books are never selected?
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?
A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has (i) no girl?
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: at least 3 girls?
Write \[\sum^m_{r = 0} \ ^{n + r}{}{C}_r\] in the simplified form.
If nC12 = nC8 , then n =
There are 12 points in a plane. The number of the straight lines joining any two of them when 3 of them are collinear, is
How many different committees of 5 can be formed from 6 men and 4 women on which exact 3 men and 2 women serve?
(a) 6
(b) 20
(c) 60
(d) 120
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
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is
Find n if `""^6"P"_2 = "n" ""^6"C"_2`
A student finds 7 books of his interest, but can borrow only three books. He wants to borrow Chemistry part II book only if Chemistry Part I can also be borrowed. Find the number of ways he can choose three books that he wants to borrow.
In how many ways a committee consisting of 3 men and 2 women, can be chosen from 7 men and 5 women?
If nCr – 1 = 36, nCr = 84 and nCr + 1 = 126, then find rC2.
A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has at least one boy and one girl
A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has at least three girls.
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 ______.
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 ______.
Three balls are drawn from a bag containing 5 red, 4 white and 3 black balls. The number of ways in which this can be done if at least 2 are red is ______.
A badminton club has 10 couples as members. They meet to organise a mixed double match. If each wife refers to p artner as well as oppose her husband in the match, then the number of different ways can the match off will be ______.
