Advertisements
Advertisements
प्रश्न
If 16Cr = 16Cr + 2, find rC4.
Advertisements
उत्तर
Given:
\[ \Rightarrow 2r = 14\]
\[ \Rightarrow r = 7\]
[∵\[{}^n C_r = \frac{n}{r} . {}^{n - 1} C_{r - 1}\]]
APPEARS IN
संबंधित प्रश्न
How many chords can be drawn through 21 points on a circle?
Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.
In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?
How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?
Compute:
(i)\[\frac{30!}{28!}\]
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 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?
If 18Cx = 18Cx + 2, find x.
If 8Cr − 7C3 = 7C2, find r.
In how many ways can a student choose 5 courses out of 9 courses if 2 courses are compulsory for every student?
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.
From a class of 12 boys and 10 girls, 10 students are to be chosen for a competition; at least including 4 boys and 4 girls. The 2 girls who won the prizes last year should be included. In how many ways can the selection be made?
How many different selections of 4 books can be made from 10 different books, if
two particular books are always selected;
There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points.
How many triangles can be obtained by joining 12 points, five of which are collinear?
Find the number of (ii) triangles
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 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.
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.
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: atmost 3 girls?
Find the number of combinations and permutations of 4 letters taken from the word 'EXAMINATION'.
If nCr + nCr + 1 = n + 1Cx , then x =
If 43Cr − 6 = 43C3r + 1 , then the value of r is
The number of diagonals that can be drawn by joining the vertices of an octagon is
Find the number of ways of dividing 20 objects in three groups of sizes 8, 7, and 5.
In how many ways a committee consisting of 3 men and 2 women, can be chosen from 7 men and 5 women?
How many committee of five persons with a chairperson can be selected from 12 persons.
There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated.
A committee of 6 is to be chosen from 10 men and 7 women so as to contain atleast 3 men and 2 women. In how many different ways can this be done if two particular women refuse to serve on the same committee ______.
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.
The number of positive integers satisfying the inequality `""^(n+1)C_(n-2) - ""^(n+1)C_(n-1) ≤ 100` is ______.
If number of arrangements of letters of the word "DHARAMSHALA" taken all at a time so that no two alike letters appear together is (4a.5b.6c.7d), (where a, b, c, d ∈ N), then a + b + c + d is equal to ______.
Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear is ______.
There are ten boys B1, B2, ...., B10 and five girls G1, G2, ...., G5 in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both B1 and B2 together should not be the members of a group is ______.
