Advertisements
Advertisements
Question
If P (9, r) = 3024, find r.
Advertisements
Solution
P (9, r) = 3024
\[ \Rightarrow \frac{9!}{\left( 9 - r \right)!} = 9 \times 8 \times 7 \times 6\]
\[ \Rightarrow \frac{9!}{\left( 9 - r \right)!} = \frac{9 \times 8 \times 7 \times 6 \times 5!}{5!}\]
\[ \Rightarrow \frac{9!}{\left( 9 - r \right)!} = \frac{9!}{5!}\]
\[ \Rightarrow \left( 9 - r \right)! = 5!\]
\[ \Rightarrow 9 - r = 5\]
\[ \Rightarrow r = 4\]
APPEARS IN
RELATED QUESTIONS
Convert the following products into factorials:
3 · 6 · 9 · 12 · 15 · 18
If (n + 1)! = 90 [(n − 1)!], find n.
If (n + 3)! = 56 [(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 n +5Pn +1 =\[\frac{11 (n - 1)}{2}\]n +3Pn, find n.
In how many ways can five children stand in a queue?
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 words, with or without meaning, can be formed by using the letters of the word 'TRIANGLE'?
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 numbers can be formed by using the digits 1 to 9 if no digit 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?
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 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
each word begins with E?
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?
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
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 with the letters of the word 'PARALLEL' so that all L's do not come together?
How many words can be formed by arranging the letters of the word 'MUMBAI' so that all M's come together?
How many number of four digits can be formed with the digits 1, 3, 3, 0?
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?
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?
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S's are together?
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'.
In how many ways can the letters of the word "INTERMEDIATE" be arranged so that:
the relative order of vowels and consonants do not alter?
Prove that the product of 2n consecutive negative integers is divisible by (2n)!
Find the number of permutations of n different things taken r at a time such that two specified things occur together?
Write the number of diagonals of an n-sided polygon.
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.
