Advertisements
Advertisements
प्रश्न
Convert the following products into factorials:
(n + 1) (n + 2) (n + 3) ... (2n)
Advertisements
उत्तर
\[\ \left( n + 1 \right)\left( n + 2 \right)\left( n + 3 \right) . . . \left( 2n \right) = \frac{\left( 1 \right)\left( 2 \right)\left( 3 \right) . . . \left( n \right)\left( n + 1 \right)\left( n + 2 \right)\left( n + 3 \right) . . . \left( 2n \right)}{\left( 1 \right)\left( 2 \right)\left( 3 \right) . . . \left( n \right)}\]
\[ = \frac{\left( 2n \right)}{n!}\]
APPEARS IN
संबंधित प्रश्न
Convert the following products into factorials:
5 · 6 · 7 · 8 · 9 · 10
Prove that: n! (n + 2) = n! + (n + 1)!
If (n + 2)! = 60 [(n − 1)!], find n.
If (n + 3)! = 56 [(n + 1)!], find n.
Prove that:
If P (5, r) = P (6, r − 1), find r ?
If 5 P(4, n) = 6. P (5, n − 1), find n ?
If nP4 = 360, find the value of 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.
If P (15, r − 1) : P (16, r − 2) = 3 : 4, find r.
If n +5Pn +1 =\[\frac{11 (n - 1)}{2}\]n +3Pn, find n.
How many words, with or without meaning, can be formed by using the letters of the word 'TRIANGLE'?
There are two works each of 3 volumes and two works each of 2 volumes; In how many ways can the 10 books be placed on a shelf so that the volumes of the same work are not separated?
If a denotes the number of permutations of (x + 2) things taken all at a time, b the number of permutations of x things taken 11 at a time and c the number of permutations of x − 11 things taken all at a time such that a = 182 bc, find the value of x.
In how many ways can the letters of the word 'STRANGE' be arranged so that
the vowels come together?
How many words can be formed out of the letters of the word, 'ORIENTAL', so that the vowels always occupy the odd places?
How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:
the letter G always occupies the first place?
How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:
the vowels always occupy even places?
How many permutations can be formed by the letters of the word, 'VOWELS', when
there is no restriction on letters?
How many permutations can be formed by the letters of the word, 'VOWELS', when
all vowels come together?
In how many ways can a lawn tennis mixed double be made up from seven married couples if no husband and wife play in the same set?
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 but first is vowel.
Find the number of words formed by permuting all the letters of the following words:
ARRANGE
Find the number of words formed by permuting all the letters of the following words:
INDIA
Find the number of words formed by permuting all the letters of the following words:
CONSTANTINOPLE
How many words can be formed with the letters of the word 'UNIVERSITY', the vowels remaining together?
How many different numbers, greater than 50000 can be formed with the digits 0, 1, 1, 5, 9.
How many numbers greater than 1000000 can be formed by using the digits 1, 2, 0, 2, 4, 2, 4?
If the letters of the word 'MOTHER' are written in all possible orders and these words are written out as in a dictionary, find the rank of the word 'MOTHER'.
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:
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.
Write the maximum number of points of intersection of 8 straight lines in a plane.
Write the number of ways in which 5 red and 4 white balls can be drawn from a bag containing 10 red and 8 white balls.
Write the total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants.
