Advertisements
Advertisements
प्रश्न
If `""^10"P"_("r" - 1)` = 2 × 6Pr, find r
उत्तर
`""^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
संबंधित प्रश्न
How many 4-digit numbers are there with no digit repeated?
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:
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.
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 ?
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?
Find the number of ways in which 8 distinct toys can be distributed among 5 childrens.
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?
Evaluate each of the following:
8P3
If the letters of the word KRISNA are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word KRISNA is
A 5-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done 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?
How many five digits telephone numbers can be constructed using the digits 0 to 9 If each number starts with 67 with no digit appears more than once?
Find the number of arrangements that can be made out of the letters of the word “ASSASSINATION”.
8 women and 6 men are standing in a line. How many arrangements are possible if any individual can stand in any position?
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
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?
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 the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is ______.
