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
Evaluate 8!
Find r if `""^5P_r = 2^6 P_(r-1)`
A coin is tossed three times and the outcomes are recorded. How many possible outcomes are there? How many possible outcomes if the coin is tossed four times? Five times? n times?
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?
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.
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 words that can be formed out of the letters of the word "ARTICLE" so that vowels occupy even places 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
Find x if `1/(6!) + 1/(7!) = x/(8!)`
If (n+2)! = 60[(n–1)!], find n
In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?
Find the rank of the word ‘CHAT’ in the dictionary.
Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time?
8 women and 6 men are standing in a line. How many arrangements are possible if any individual can stand in any position?
If the letters of the word FUNNY are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, find the rank of the word FUNNY
How many words can be formed with the letters of the word MANAGEMENT by rearranging them?
In how many ways can 5 children be arranged in a line such that two particular children of them are always together
In how many ways 3 mathematics books, 4 history books, 3 chemistry books and 2 biology books can be arranged on a shelf so that all books of the same subjects are together.
Find the number of permutations of n different things taken r at a time such that two specific things occur together.
