Advertisements
Advertisements
प्रश्न
If P (5, r) = P (6, r − 1), find r ?
Advertisements
उत्तर
P (5, r) = P (6, r − 1)
or 5Pr = 6Pr-1
\[\frac{5!}{\left( 5 - r \right)!} = \frac{6!}{\left( 6 - r + 1 \right)!}\]
\[ \Rightarrow \frac{\left( 6 - r + 1 \right)!}{\left( 5 - r \right)!} = \frac{6!}{5!}\]
\[ \Rightarrow \frac{(7 - r)!}{\left( 5 - r \right)!} = \frac{6\left( 5! \right)}{5!}\]
\[ \Rightarrow \frac{\left( 7 - r \right)\left( 6 - r \right)\left( 5 - r \right)!}{\left( 5 - r \right)!} = 6\]
\[ \Rightarrow \left( 7 - r \right)\left( 6 - r \right) = 6\]
\[ \Rightarrow \left( 7 - r \right)\left( 6 - r \right) = 3 \times 2\]
\[\text{On comparing the above two equations, we get}: \]
\[7 - r = 3\]
\[ \Rightarrow r = 4\]
APPEARS IN
संबंधित प्रश्न
Convert the following products into factorials:
3 · 6 · 9 · 12 · 15 · 18
If (n + 2)! = 60 [(n − 1)!], find n.
If (n + 1)! = 90 [(n − 1)!], 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 (2n − 1, n) : P (2n + 1, n − 1) = 22 : 7 find n.
If P (15, r − 1) : P (16, r − 2) = 3 : 4, find r.
How many words, with or without meaning, can be formed by using the letters of the word 'TRIANGLE'?
How many three-digit numbers are there, with no digit repeated?
In how many ways can 6 boys and 5 girls be arranged for a group photograph if the girls are to sit on chairs in a row and the boys are to stand in a row behind them?
How many 3-digit even number can be made using the digits 1, 2, 3, 4, 5, 6, 7, if no digits is 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?
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
each word begins with E?
How many permutations can be formed by the letters of the word, 'VOWELS', when
each word begins with O and ends with L?
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?
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\[\frac{m! (m + 1)!}{(m - n + 1) !}\]
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 4 letters are used at a time?
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.
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
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?
Find the total number of permutations of the letters of the word 'INSTITUTE'.
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.
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'?
For all positive integers n, show that 2nCn + 2nCn − 1 = `1/2` 2n + 2Cn+1
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 at a time
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?
How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?
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.
