Advertisements
Advertisements
प्रश्न
Find n and r if `""^"n""P"_"r"` = 720 and `""^"n""C"_("n" - "r")` = 120
Advertisements
उत्तर
`""^"n""P"_"r"` = 720
∴ `("n"!)/(("n" - "r")!)` = 720 ...(i)
Also, `""^"n""C"_("n" - "r")` = 120
∴ `("n"!)/(("n" - "r")!("n"-"n"+"r")!) = 120`
∴ `("n"!)/("r"!("n" - "r")!)` = 120 ...(ii)
Dividing (i) by (ii), we get
∴ `(("n"!)/(("n"-"r")!))/(("n"!)/("r"!("n"-"r")!))=720/120`
∴ r! = 6
∴ r = 3
Substituting r = 3 in (i), we get
∴ `("n"!)/(("n" - 3)!)` = 720
∴ `("n"("n" - 1)("n" - 2)("n" - 3)!)/(("n" - 3)!)` = 720
∴ n(n – 1)(n – 2) = 10 × 9 × 8
∴ n = 10
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?
In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?
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?
In how many ways can an examinee answer a set of ten true/false type questions?
How many three-digit odd numbers are there?
Evaluate the following:
14C3
If 15C3r = 15Cr + 3, find r.
If 28C2r : 24C2r − 4 = 225 : 11, find r.
If α = mC2, then find the value of αC2.
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.
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?
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(iii) at least 3 girls?
If nC12 = nC8 , then n =
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is
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?
We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can selections be made?
There are 10 professors and 20 lecturers out of whom a committee of 2 professors and 3 lecturer is to be formed. Find:
| C1 | C2 |
| (a) In how many ways committee: can be formed | (i) 10C2 × 19C3 |
| (b) In how many ways a particular: professor is included | (ii) 10C2 × 19C2 |
| (c) In how many ways a particular: lecturer is included | (iii) 9C1 × 20C3 |
| (d) In how many ways a particular: lecturer is excluded | (iv) 10C2 × 20C3 |
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 ______.
A regular polygon has 20 sides. The number of triangles that can be drawn by using the vertices but not using the sides is
