English

If 35cn +7 = 35c4n − 2 , Then Write the Values of N.

Advertisements
Advertisements

Question

If 35Cn +7 = 35C4n − 2 , then write the values of n.

Advertisements

Solution

 35Cn +7 = 35C4n − 2 

\[n + 7 + 4n - 2 = 35\]   [∵\[{}^n C_x =^n C_y \Rightarrow n = x + y\ \text{or} x = y\]]
\[\Rightarrow 5n = 30\]
\[ \Rightarrow n = 6\]
\[\text{And}, n + 7 = 4n - 2\]
\[ \Rightarrow n = 3\]
shaalaa.com
Factorial N (N!) Permutations and Combinations
  Is there an error in this question or solution?
Chapter 17: Combinations - Exercise 17.4 [Page 24]

APPEARS IN

R.D. Sharma Mathematics [English] Class 11
Chapter 17 Combinations
Exercise 17.4 | Q 2 | Page 24

RELATED QUESTIONS

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)


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 ?


If P (n, 5) = 20. P(n, 3), find n ?


If P(11, r) = P (12, r − 1) find r.


If P (n, 4) = 12 . P (n, 2), find n.


If P (2n − 1, n) : P (2n + 1, n − 1) = 22 : 7 find n.


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


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?


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?


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

the vowels come together?

 


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 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

all vowels 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 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:
INTERMEDIATE


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 numbers can be formed with the digits 1, 2, 3, 4, 3, 2, 1 so that the odd digits always occupy the odd places?


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


Find the number of numbers, greater than a million, that can be formed with the digits 2, 3, 0, 3, 4, 2, 3.


In how many ways can the letters of the word ASSASSINATION be arranged so that all the S's are together?


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'.


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'?


Prove that the product of 2n consecutive negative integers is divisible by (2n)!


Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
n · n − 1Cr − 1 = (n − r + 1) nCr − 1


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

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

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 


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


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.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×