Advertisements
Advertisements
प्रश्न
If P(11, r) = P (12, r − 1) find r.
Advertisements
उत्तर
P(11, r) = P (12, r − 1)
\[ \Rightarrow \frac{\left( 13 - r \right)}{\left( 11 - r \right)!} = \frac{12!}{11!}\]
\[ \Rightarrow \frac{\left( 13 - r \right)\left( 12 - r \right)\left( 11 - r \right)!}{\left( 11 - r \right)!} = \frac{12 \times 11!}{11!}\]
\[ \Rightarrow \left( 13 - r \right)\left( 12 - r \right) = 12\]
\[ \Rightarrow \left( 13 - r \right)\left( 12 - r \right) = 4 \times 3\]
\[\text{On comparing the two sides, we get}: \]
\[13 - r = 4\]
\[ \Rightarrow r = 9\]
APPEARS IN
संबंधित प्रश्न
Prove that: n! (n + 2) = n! + (n + 1)!
If P (n, 5) = 20. P(n, 3), find n ?
If nP4 = 360, find the value of n.
If P (n − 1, 3) : P (n, 4) = 1 : 9, find n.
Prove that:1 . P (1, 1) + 2 . P (2, 2) + 3 . P (3, 3) + ... + n . P (n, n) = P (n + 1, n + 1) − 1.
From among the 36 teachers in a school, one principal and one vice-principal are to be appointed. In how many ways can this be done?
Four books, one each in Chemistry, Physics, Biology and Mathematics, are to be arranged in a shelf. In how many ways can this be done?
How many three-digit numbers are there, with distinct digits, with each digit odd?
How many three-digit numbers are there, with no digit repeated?
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?
All the letters of the word 'EAMCOT' are arranged in different possible ways. Find the number of arrangements in which no two vowels are adjacent to each other.
In how many ways can the letters of the word 'STRANGE' be arranged so that
the vowels occupy only the odd places?
How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:
the letters P and I respectively occupy first and last place?
How many permutations can be formed by the letters of the word, 'VOWELS', when
each word begins with E?
How many words (with or without dictionary meaning) can be made from the letters in the word MONDAY, assuming that no letter is repeated, if all letters are used at a time.
Find the number of words formed by permuting all the letters of the following words:
INTERMEDIATE
Find the number of words formed by permuting all the letters of the following words:
SERIES
How many words can be formed with the letters of the word 'UNIVERSITY', the vowels remaining together?
Find the total number of arrangements of the letters in the expression a3 b2 c4 when written at full length.
How many words can be formed by arranging the letters of the word 'MUMBAI' so that all M's come together?
How many different signals can be made from 4 red, 2 white and 3 green flags by arranging all of them vertically on a flagstaff?
How many words can be formed from the letters of the word 'SERIES' which start with S and end with S?
Find the number of numbers, greater than a million, that can be formed with the digits 2, 3, 0, 3, 4, 2, 3.
There are three copies each of 4 different books. In how many ways can they be arranged in a shelf?
A biologist studying the genetic code is interested to know the number of possible arrangements of 12 molecules in a chain. The chain contains 4 different molecules represented by the initials A (for Adenine), C (for Cytosine), G (for Guanine) and T (for Thymine) and 3 molecules of each kind. How many different such arrangements are possible?
How many numbers greater than 1000000 can be formed by using the digits 1, 2, 0, 2, 4, 2, 4?
If the permutations of a, b, c, d, e taken all together be written down in alphabetical order as in dictionary and numbered, find the rank of the permutation debac ?
The letters of the word 'ZENITH' are written in all possible orders. How many words are possible if all these words are written out as in a dictionary? What is the rank of the word 'ZENITH'?
Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
How many words, with or without meaning can be formed from the letters of the word 'MONDAY', assuming that no letter is repeated, if (i) 4 letters are used at a time
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
Find the number of permutations of n different things taken r at a time such that two specified things occur together?
Write the maximum number of points of intersection of 8 straight lines in a plane.
Write the number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines.
