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 4! – 3!
Evaluate `(n!)/((n-r)!)`, when n = 9, r = 5
Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even?
From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?
Find r if `""^5P_r = 2^6 P_(r-1)`
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 of the distinct permutations of the letters in MISSISSIPPI do the four I’s not come together?
A customer forgets a four-digits code for an Automatic Teller Machine (ATM) in a bank. However, he remembers that this code consists of digits 3, 5, 6 and 9. Find the largest possible number of trials necessary to obtain the correct code.
In how many ways can 5 different balls be distributed among three boxes?
In how many ways can 7 letters be posted in 4 letter boxes?
Evaluate each of the following:
6P6
The number of words from the letters of the word 'BHARAT' in which B and H will never come together, is
The number of arrangements of the letters of the word BHARAT taking 3 at a time is
How many six-digit telephone numbers can be formed if the first two digits are 45 and no digit can appear more than once?
- In how many ways can 8 identical beads be strung on a necklace?
- In how many ways can 8 boys form a ring?
Find the rank of the word ‘CHAT’ in the dictionary.
The possible outcomes when a coin is tossed five times:
If `""^10"P"_("r" - 1)` = 2 × 6Pr, find r
A test consists of 10 multiple choice questions. In how many ways can the test be answered if each question has four 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.
What is the maximum number of different answers can the students give?
A coin is tossed 8 times, how many different sequences of heads and tails are possible?
A coin is tossed 8 times, how many different sequences containing six heads and two 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?
In how many ways can 5 children be arranged in a line such that two particular children of them are never together.
The number of signals that can be sent by 6 flags of different colours taking one or more at a time is ______.
A five-digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5 without repetitions. The total number of ways this can be done is ______.
The number of permutations of n different objects, taken r at a line, when repetitions are allowed, is ______.
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 ______.
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Determine the number of words which have at least one letter repeated.
If m+nP2 = 90 and m–nP2 = 30, then (m, n) is given by ______.
