मराठी

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)\[\times\]( 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
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 16: Permutations - Exercise 16.1 [पृष्ठ ४]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
पाठ 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)


If (n + 1)! = 90 [(n − 1)!], find n.


If (n + 3)! = 56 [(n + 1)!], find n.


Prove that: 

\[\frac{n!}{(n - r)!}\] = n (n − 1) (n − 2) ... (n − (r − 1))

If P (n, 4) = 12 . P (n, 2), find n.


If P (n − 1, 3) : P (n, 4) = 1 : 9, find n.


If P (n, 5) : P (n, 3) = 2 : 1, find n.


Prove that:1 . P (1, 1) + 2 . P (2, 2) + 3 . P (3, 3) + ... + n . P (nn) = P (n + 1, n + 1) − 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 letters E, K, S and V, one in each, were purchased from a plastic warehouse. How many ordered pairs of letters, to be used as initials, can be formed from them?


How many three-digit numbers are there, with distinct digits, with each digit odd?


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?


How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:

the letters P and I respectively occupy first and last place?


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?


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 consonants come together?


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 three letter words can be made using the letters of the word 'ORIENTAL'?


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 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 permutations of the letters of the word 'MADHUBANI' do not begin with M but end with I?


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?


Evaluate

\[^ {20}{}{C}_5 + \sum^5_{r = 2} {}^{25 - r} C_4\]

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 


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 maximum number of points of intersection of 8 straight lines in a plane.


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 number of ways in which 12 boys may be divided into three groups of 4 boys each.


Write the total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×