हिंदी

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

Advertisements
Advertisements

प्रश्न

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

Advertisements

उत्तर

 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
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 17: Combinations - Exercise 17.4 [पृष्ठ २४]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 17 Combinations
Exercise 17.4 | Q 2 | पृष्ठ २४

संबंधित प्रश्न

Convert the following products into factorials:

5 · 6 · 7 · 8 · 9 · 10


Convert the following products into factorials: 

3 · 6 · 9 · 12 · 15 · 18


If (n + 3)! = 56 [(n + 1)!], find n.


If P (9, r) = 3024, find r.


If P (n, 4) = 12 . P (n, 2), find n.


Prove that:1 . P (1, 1) + 2 . P (2, 2) + 3 . P (3, 3) + ... + n . P (n, n) = P (n + 1, n + 1) − 1.


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 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?


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 '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 never come together? 


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 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 permutations can be formed by the letters of the word, 'VOWELS', when

each word begins with O and ends with L?


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 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?


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:

INDIA


Find the number of words formed by permuting all the letters of the following words:
EXERCISES


Find the number of words formed by permuting all the letters of the following words:
CONSTANTINOPLE


In how many ways can the letters of the word 'ALGEBRA' be arranged without changing the relative order of the vowels and consonants?


How many words can be formed with the letters of the word 'UNIVERSITY', the vowels remaining together?


How many words can be formed with the letters of the word 'PARALLEL' so that all L's do not come together?


How many number of four digits can be formed with the digits 1, 3, 3, 0?


How many different numbers, greater than 50000 can be formed with the digits 0, 1, 1, 5, 9.


How many words can be formed from the letters of the word 'SERIES' which start with S and end with S?


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?


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

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

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

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

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


How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?


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.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×