Advertisements
Advertisements
प्रश्न
If P (n, 4) = 12 . P (n, 2), find n.
Advertisements
उत्तर
P (n, 4) = 12 . P (n, 2)
\[\Rightarrow \frac{n!}{\left( n - 4 \right)!} = 12 \times \frac{n!}{\left( n - 2 \right)!}\]
\[ \Rightarrow \frac{\left( n - 2 \right)!}{\left( n - 4 \right)!} = 12 \times \frac{n!}{n!}\]
\[ \Rightarrow \frac{\left( n - 2 \right)\left( n - 3 \right)\left( n - 4 \right)!}{\left( n - 4 \right)!} = 12\]
\[ \Rightarrow \left( n - 2 \right)\left( n - 3 \right) = 12\]
\[ \Rightarrow \left( n - 2 \right)\left( n - 3 \right) = 4 \times 3\]
\[\text{On comparing the LHS and the RHS, we get}: \]
\[n - 2 = 4\]
\[ \Rightarrow n = 6\]
APPEARS IN
संबंधित प्रश्न
Convert the following products into factorials:
3 · 6 · 9 · 12 · 15 · 18
Convert the following products into factorials:
(n + 1) (n + 2) (n + 3) ... (2n)
If (n + 1)! = 90 [(n − 1)!], find n.
If \[\frac{(2n)!}{3! (2n - 3)!}\] and \[\frac{n!}{2! (n - 2)!}\] are in the ratio 44 : 3, find n.
Prove that:
\[\frac{n!}{(n - r)! r!} + \frac{n!}{(n - r + 1)! (r - 1)!} = \frac{(n + 1)!}{r! (n - r + 1)!}\]
If P (n, 5) = 20. P(n, 3), find n ?
In how many ways can five children stand in a queue?
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?
How many 6-digit telephone numbers can be constructed with digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each number starts with 35 and no digit appears more than once?
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?
In how many ways can the letters of the word 'STRANGE' be arranged so that
the vowels never come together?
How many words can be formed from the letters of the word 'SUNDAY'? How many of these begin with D?
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 with the letters of word 'SUNDAY'? How many of the words begin with N? How many begin with N and end in Y?
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 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?
How many permutations can be formed by the letters of the word, 'VOWELS', when
all consonants 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 three letter words can be made using the letters of the word 'ORIENTAL'?
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
How many words can be formed with the letters of the word 'UNIVERSITY', the vowels remaining together?
How many words can be formed with the letters of the word 'PARALLEL' so that all L's do not come together?
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?
The letters of the word 'SURITI' are written in all possible orders and these words are written out as in a dictionary. Find the rank of the word 'SURITI'.
Find the total number of ways in which six ‘+’ and four ‘−’ signs can be arranged in a line such that no two ‘−’ signs occur together.
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.
How many words, with or without meaning can be formed from the letters of the word 'MONDAY', assuming that no letter is repeated, if all letters are used but first letter is a vowel?
Write the expression nCr +1 + nCr − 1 + 2 × nCr in the simplest form.
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.
