हिंदी

If (N + 2)! = 60 [(N − 1)!], Find N.

Advertisements
Advertisements

प्रश्न

If (n + 2)! = 60 [(n − 1)!], find n. 

Advertisements

उत्तर

(n + 2)! = 60 [(n − 1)!]

\[\Rightarrow\](n + 2)\[\times\](n + 1)\[\times\](n)\[\times\](n − 1)! = 60 [(n − 1)!]
\[\Rightarrow\](n + 2)\[\times\](n + 1)\[\times\](n) = 60
\[\Rightarrow\](n + 2)\[\times\](n + 1)\[\times\](n) = 5\[\times\]4\[\times\]3

∴ n = 3


shaalaa.com
Factorial N (N!) Permutations and Combinations
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 16: Permutations - Exercise 16.1 [पृष्ठ ४]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 16 Permutations
Exercise 16.1 | Q 7 | पृष्ठ ४

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)


Convert the following products into factorials:

1 · 3 · 5 · 7 · 9 ... (2n − 1)


If (n + 3)! = 56 [(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 ?


If P (n, 4) = 12 . P (n, 2), find n.


If P (15, r − 1) : P (16, r − 2) = 3 : 4, find r.


In how many ways can five children stand in a queue?


Find the number of different 4-letter words, with or without meanings, that can be formed from the letters of the word 'NUMBER'.


How many three-digit numbers are there, with no digit repeated?


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 come together?

 


In how many ways can the letters of the word 'STRANGE' be arranged so that

the vowels occupy only the odd places?


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 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 O and ends with L?


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 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 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 different signals can be made from 4 red, 2 white and 3 green flags by arranging all of them vertically on a flagstaff?


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 'LATE' be permuted and the words so formed be arranged as in a dictionary, find the rank of the word LATE.


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.


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: 4nC2n : 2nCn = [1 · 3 · 5 ... (4n − 1)] : [1 · 3 · 5 ... (2n − 1)]2.


Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:

\[\frac{^{n}{}{C}_r}{^{n}{}{C}_{r - 1}} = \frac{n - r + 1}{r}\]

Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.


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 parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×