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
Convert the following products into factorials:
1 · 3 · 5 · 7 · 9 ... (2n − 1)
Prove that:
If P (5, r) = P (6, r − 1), find r ?
If nP4 = 360, find the value of n.
If P (n, 4) = 12 . P (n, 2), find n.
If P (2n − 1, n) : P (2n + 1, n − 1) = 22 : 7 find n.
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 all the letters of the word 'DELHI', using each letter exactly once?
How many words, with or without meaning, can be formed by using the letters of the word 'TRIANGLE'?
How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
How many 3-digit even number can be made using the digits 1, 2, 3, 4, 5, 6, 7, if no digits is repeated?
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 'FAILURE' be arranged so that the consonants may occupy only odd positions?
In how many ways can the letters of the word 'STRANGE' be arranged so that
the vowels never come together?
How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:
the vowels are always together?
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?
m men and n women are to be seated in a row so that no two women sit together. if m > n then show that the number of ways in which they can be seated as\[\frac{m! (m + 1)!}{(m - n + 1) !}\]
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:
PAKISTAN
Find the number of words formed by permuting all the letters of the following words:
SERIES
Find the number of words formed by permuting all the letters of the following words:
EXERCISES
Find the number of words formed by permuting all the letters of the following words:
CONSTANTINOPLE
In how many ways can the letters of the word 'ALGEBRA' be arranged without changing the relative order of the vowels and consonants?
How many number of four digits can be formed with the digits 1, 3, 3, 0?
In how many ways can the letters of the word 'ARRANGE' be arranged so that the two R's are never together?
How many permutations of the letters of the word 'MADHUBANI' do not begin with M but end with I?
There are three copies each of 4 different books. In how many ways can they be arranged in a shelf?
How many different arrangements can be made by using all the letters in the word 'MATHEMATICS'. How many of them begin with C? How many of them begin with T?
Prove that the product of 2n consecutive negative integers is divisible by (2n)!
Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
There are 10 persons named\[P_1 , P_2 , P_3 , . . . . , P_{10}\]
Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements.
Write the value of\[\sum^6_{r = 1} \ ^{56 - r}{}{C}_3 + \ ^ {50}{}{C}_4\]
Write the number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines.
Write the total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants.
