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 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, 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!)
Twelve students complete in a race. In how many ways first three prizes be given?
How many three-digit numbers are there with no digit repeated?
If 18Cx = 18Cx + 2, find x.
If 15Cr : 15Cr − 1 = 11 : 5, find r.
Find the number of diagonals of (ii) a polygon of 16 sides.
How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?
Find n if `""^6"P"_2 = "n" ""^6"C"_2`
There are 20 straight lines in a plane so that no two lines are parallel and no three lines are concurrent. Determine the number of points of intersection.
A student has to answer 10 questions, choosing atleast 4 from each of Parts A and B. If there are 6 questions in Part A and 7 in Part B, in how many ways can the student choose 10 questions?
In a small village, there are 87 families, of which 52 families have atmost 2 children. In a rural development programme 20 families are to be chosen for assistance, of which atleast 18 families must have at most 2 children. In how many ways can the choice be made?
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 ______.
15C8 + 15C9 – 15C6 – 15C7 = ______.
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 ______.
The number of numbers between 2,000 and 5,000 that can be formed with the digits 0, 1, 2, 3, 4, (repetition of digits is not allowed) and are multiple of 3 is?
The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike is ______.
