मराठी

Prove That: N! (N + 2) = N! + (N + 1)! - Mathematics

Advertisements
Advertisements

प्रश्न

Prove that: n! (n + 2) = n! + (n + 1)!

उत्तर

RHS = n! + (n + 1)!
        =  n! + (n + 1)(n!)
        = n! ( 1+ n + 1)
        = n! (n+2) = LHS
Hence, proved.

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

आरडी शर्मा Mathematics [English] Class 11
पाठ 16 Permutations
Exercise 16.1 | Q 6 | 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 + 2)! = 60 [(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 (5, r) = P (6, r − 1), find r ?


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?


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?


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?


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

the vowels never 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 from the letters of the word 'SUNDAY'? How many of these begin with D?


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

the letter G always occupies the first place?


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
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 consonants come together?


How many words can be formed out of the letters of the word 'ARTICLE', so that vowels occupy even places?


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 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:

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:

RUSSIA


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 from the letters of the word 'SERIES' which start with S and end with S?


In how many ways can 4 red, 3 yellow and 2 green discs be arranged in a row if the discs of the same colour are indistinguishable?


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.


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 (i) 4 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?


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.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×