हिंदी

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?

Advertisements
Advertisements

प्रश्न

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?

Advertisements

उत्तर

Number of arrangements of the boys = Number of arrangements of the 6 boys taken 6 at a time = 6!
Number of arrangements of the girls = Number of arrangements of the 5 girls taken 5 at a time = 5!
Total number of arrangements = 6! x 5! = 86400

shaalaa.com
Factorial N (N!) Permutations and Combinations
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 16: Permutations - Exercise 16.3 [पृष्ठ २९]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 16 Permutations
Exercise 16.3 | Q 27 | पृष्ठ २९

संबंधित प्रश्न

Convert the following products into factorials: 

(n + 1) (n + 2) (n + 3) ... (2n)


If (n + 2)! = 60 [(n − 1)!], find n. 


Prove that:

\[\frac{(2n + 1)!}{n!}\] = 2n [1 · 3 · 5 ... (2n − 1) (2n + 1)]

If P (5, r) = P (6, r − 1), find r ?


If 5 P(4, n) = 6. P (5, n − 1), find n ?


If nP4 = 360, find the value of n.


If P(11, r) = P (12, r − 1) find r.


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


If n +5Pn +1 =\[\frac{11 (n - 1)}{2}\]n +3Pn, find n.


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?


Four books, one each in Chemistry, Physics, Biology and Mathematics, are to be arranged in a shelf. In how many ways can this be done?


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 distinct digits, with each digit odd?


There are 6 items in column A and 6 items in column B. A student is asked to match each item in column A with an item in column B. How many possible, correct or incorrect, answers are there to this question?


How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?


How many 3-digit even number can be made using the digits 1, 2, 3, 4, 5, 6, 7, if no digits is repeated?


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

the vowels never come together? 


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

there is no restriction on letters?


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


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.


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


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


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


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


Find the total number of permutations of the letters of the word 'INSTITUTE'.


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.


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


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:

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

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

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

Write the number of diagonals of an n-sided polygon.


Write the value of\[\sum^6_{r = 1} \ ^{56 - r}{}{C}_3 + \ ^ {50}{}{C}_4\]


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


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×