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
Compute `(8!)/(6! xx 2!)`
Which of the following are true:
(2 +3)! = 2! + 3!
Which of the following are true:
(2 × 3)! = 2! × 3!
How many numbers of four digits can be formed with the digits 1, 2, 3, 4, 5 if the digits can be repeated in the same number?
Find the total number of ways in which 20 balls can be put into 5 boxes so that first box contains just one ball ?
In how many ways can 4 prizes be distributed among 5 students, when
(i) no student gets more than one prize?
(ii) a student may get any number of prizes?
(iii) no student gets all the prizes?
Write the total number of possible outcomes in a throw of 3 dice in which at least one of the dice shows an even number.
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 6 men and 5 women can dine at a round table if no two women sit together ?
Write the remainder obtained when 1! + 2! + 3! + ... + 200! is divided by 14 ?
The number of permutations of n different things taking r at a time when 3 particular things are to be included is
The number of ways in which 6 men can be arranged in a row so that three particular men are consecutive, is
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
The number of ways in which the letters of the word ARTICLE can be arranged so that even places are always occupied by consonants is
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 5 and r = 2.
Evaluate the following.
`(3! + 1!)/(2^2!)`
The possible outcomes when a coin is tossed five times:
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
Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if each question has four choices?
8 women and 6 men are standing in a line. How many arrangements are possible if any individual can stand in any position?
8 women and 6 men are standing in a line. In how many arrangements will no two men be standing next to one another?
A coin is tossed 8 times, how many different sequences of heads and tails are possible?
How many strings are there using the letters of the word INTERMEDIATE, if the vowels and consonants are alternative
Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number. How many distinct 6-digit numbers are there?
Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number. How many of these 6-digit numbers are even?
Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5 repetitions not allowed?
Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?
There are 10 persons named P1, P2, P3, ... P10. Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements.
In a certain city, all telephone numbers have six digits, the first two digits always being 41 or 42 or 46 or 62 or 64. How many telephone numbers have all six digits distinct?
The number of 5-digit telephone numbers having atleast one of their digits repeated 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`.
How many words (with or without dictionary meaning) can be made from the letters of the word MONDAY, assuming that no letter is repeated, if
| C1 | C2 |
| (a) 4 letters are used at a time | (i) 720 |
| (b) All letters are used at a time | (ii) 240 |
| (c) All letters are used but the first is a vowel | (iii) 360 |
Let b1, b2, b3, b4 be a 4-element permutation with bi ∈ {1, 2, 3, .......,100} for 1 ≤ i ≤ 4 and bi ≠ bj for i ≠ j, such that either b1, b2, b3 are consecutive integers or b2, b3, b4 are consecutive integers. Then the number of such permutations b1, b2, b3, b4 is equal to ______.
If 1P1 + 2. 2p2 + 3. 3p3 + ....... 15. 15P15 = qPr – s, 0 ≤ s ≤ 1, then q+sCr–s is equal to ______.
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 ______.
Number of words from the letters of the words BHARAT in which B and H will never come together is ______.
