Advertisements
Advertisements
प्रश्न
Find r if `""^5P_r = ""^6P_(r-1)`
Advertisements
उत्तर
`""^5P_r = ""^6P_(r-1)`
⇒ `(5!)/((5 - r)!) = (6!)/((6 - r + 1)!)`
⇒ `(5!)/((5 - r)!) = (6 xx 5!)/((7 - r )!)`
⇒ `1/((5 - r)!) = 6/((7 - r)(6 - r)(5 - r)!)`
⇒ 1 = `6/((7 - r)(6 - r))`
⇒ (7 - r)(6 - r) = 6
⇒ 42 - 7r - 6r + r2 - 6 = 0
⇒ r2 - 13r + 36 = 0
⇒ r2 - 4r - 9r + 36 = 0
⇒ r(r - 4 ) -9 (r - 4) = 0
⇒ r(r - 4)(r - 9) = 0
⇒ (r - 4) = 0 or (r - 9) = 0
⇒ r = 4 or r = 9
It is known that, `""^nP_r = (n!)/((n - r)!) 0 ≤ r ≤ n`
∴ 0 ≤ r ≤ 5
Hence, r ≠ 9
∴ r = 4
APPEARS IN
संबंधित प्रश्न
Evaluate `(n!)/((n-r)!)` when n = 6, r = 2
Evaluate `(n!)/((n-r)!)`, when n = 9, r = 5
How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?
Find x in each of the following:
How many natural numbers not exceeding 4321 can be formed with the digits 1, 2, 3 and 4, if the digits can repeat?
How many natural numbers less than 1000 can be formed from the digits 0, 1, 2, 3, 4, 5 when a digit may be repeated any number of times?
Find the number of ways in which one can post 5 letters in 7 letter boxes ?
In how many ways can 5 different balls be distributed among three boxes?
Write the number of ways in which 7 men and 7 women can sit on a round table such that no two women sit together ?
Write the number of ways in which 5 boys and 3 girls can be seated in a row so that each girl is between 2 boys ?
Write the remainder obtained when 1! + 2! + 3! + ... + 200! is divided by 14 ?
The number of six letter words that can be formed using the letters of the word "ASSIST" in which S's alternate with other letters is
If in a group of n distinct objects, the number of arrangements of 4 objects is 12 times the number of arrangements of 2 objects, then the number of objects is
The product of r consecutive positive integers is divisible by
If k + 5Pk + 1 =\[\frac{11 (k - 1)}{2}\]. k + 3Pk , then the values of k are
The number of words that can be made by re-arranging the letters of the word APURBA so that vowels and consonants are alternate is
English alphabet has 11 symmetric letters that appear same when looked at in a mirror. These letters are A, H, I, M, O, T, U, V, W, X and Y. How many symmetric three letters passwords can be formed using these letters?
If nP4 = 12(nP2), find n.
The total number of 9 digit number which has all different digit is:
If `""^(("n" – 1))"P"_3 : ""^"n""P"_4` = 1 : 10 find n
A test consists of 10 multiple choice questions. In how many ways can the test be answered if each question has four choices?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if the first four questions have three choices and the remaining have five choices?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if question number n has n + 1 choices?
A student appears in an objective test which contain 5 multiple choice questions. Each question has four choices out of which one correct answer.
How will the answer change if each question may have more than one correct answers?
In how many ways can the letters of the word SUCCESS be arranged so that all Ss are together?
How many strings are there using the letters of the word INTERMEDIATE, if the vowels and consonants are alternative
Choose the correct alternative:
The product of r consecutive positive integers is divisible b
If all permutations of the letters of the word AGAIN are arranged in the order as in a dictionary. What is the 49th word?
Find the number of permutations of n different things taken r at a time such that two specific things occur together.
Ten different letters of alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have atleast one letter repeated is ______.
The total number of 9 digit numbers which have all different digits is ______.
The number of words which can be formed out of the letters of the word ARTICLE, so that vowels occupy the even place is ______.
In the permutations of n things, r taken together, the number of permutations in which m particular things occur together is `""^(n - m)"P"_(r - m) xx ""^r"P"_m`.
Using the digits 1, 2, 3, 4, 5, 6, 7, a number of 4 different digits is formed. Find
| C1 | C2 |
| (a) How many numbers are formed? | (i) 840 |
| (b) How many number are exactly divisible by 2? | (i) 200 |
| (c) How many numbers are exactly divisible by 25? | (iii) 360 |
| (d) How many of these are exactly divisible by 4? | (iv) 40 |
The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is ______.
