Advertisements
Advertisements
प्रश्न
If `""^10"P"_("r" - 1)` = 2 × 6Pr, find r
Advertisements
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
In how many ways can the letters of the word PERMUTATIONS be arranged if the words start with P and end with S.
How many three digit numbers can be formed by using the digits 0, 1, 3, 5, 7 while each digit may be repeated any number of times?
In how many ways can 5 different balls be distributed among three boxes?
Write the number of words that can be formed out of the letters of the word 'COMMITTEE' ?
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
The number of ways in which 6 men can be arranged in a row so that three particular men are consecutive, 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
For all n > 0, nC1 + nC2 + nC3 + …… + nCn is equal to:
The number of words with or without meaning that can be formed using letters of the word “EQUATION”, with no repetition of letters is:
Find the distinct permutations of the letters of the word MISSISSIPPI?
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
If all permutations of the letters of the word AGAIN are arranged in the order as in a dictionary. What is the 49th word?
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
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`.
Five boys and five girls form a line. Find the number of ways of making the seating arrangement under the following condition:
| C1 | C2 |
| (a) Boys and girls alternate: | (i) 5! × 6! |
| (b) No two girls sit together : | (ii) 10! – 5! 6! |
| (c) All the girls sit together | (iii) (5!)2 + (5!)2 |
| (d) All the girls are never together : | (iv) 2! 5! 5! |
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 m+nP2 = 90 and m–nP2 = 30, then (m, n) is given by ______.
