Advertisements
Advertisements
Question
If `""^10"P"_("r" - 1)` = 2 × 6Pr, find r
Advertisements
Solution
`""^10"P"_("r" - 1)` = 2 × 6Pr
`(10!)/((10 - "r" + 1)!) = 2 xx (6!)/((6 -"r")!)`
`(10!)/(6! xx 2) = ((11 - "")!)/((6 - "r)!)`
`((11 - "r")(10 - "r")(9 - "r")(8 - "r")(7 - "r")(6 - "r")!)/((6 - "r")!) = (10xx 9 xx 8 xx 7 xx 6!)/(6! xx 2)`
⇒ `(11 - "r")(10 - "r")(9 - "r")(8 "r")(7 - "r") = 10 xx 9 xx 4 xx 7`
= `5 xx 2 xx 3 xx 3 xx 2 xx 2 xx 7`
= `7 xx 6 xx 5 xx 4 xx 3`
⇒ 11 – r = 7
11 – 7 = r
r = 4
APPEARS IN
RELATED QUESTIONS
How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?
Find r if `""^5P_r = ""^6P_(r-1)`
In how many ways can the letters of the word PERMUTATIONS be arranged if the vowels are all together.
In how many ways can the letters of the word PERMUTATIONS be arranged if the there are always 4 letters between P and S?
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?
How many numbers of six digits can be formed from the digits 0, 1, 3, 5, 7 and 9 when no digit is repeated? How many of them are divisible by 10 ?
Find the number of ways in which 8 distinct toys can be distributed among 5 childrens.
Find the rank of the word ‘CHAT’ in the dictionary.
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?
In how many ways 4 mathematics books, 3 physics books, 2 chemistry books and 1 biology book can be arranged on a shelf so that all books of the same subjects are together
How many strings are there using the letters of the word INTERMEDIATE, if the vowels and consonants are alternative
Find the number of strings that can be made using all letters of the word THING. If these words are written as in a dictionary, what will be the 85th string?
How many words can be formed with the letters of the word MANAGEMENT by rearranging them?
If all permutations of the letters of the word AGAIN are arranged in the order as in a dictionary. What is the 49th word?
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 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 ______.
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 ______.
