हिंदी

In how many ways can a lawn tennis mixed double be made up from seven married couples if no husband and wife play in the same set?

Advertisements
Advertisements

प्रश्न

In how many ways can a lawn tennis mixed double be made up from seven married couples if no husband and wife play in the same set?

योग
Advertisements

उत्तर

Let two husbands A, B be selected out of seven males in 7P2  ways. excluding their wives, we have to select two ladies C,D out of remaining 5 wives is 5P2 ways.

Thus, number of ways of selecting the players for mixed double is = 7P2 × 5P2

= 21 × 10

= 210

Now, suppose A chooses C as partner (B will automatically go to D) or A chooses 0 as partner (B will automatically go to C). Thus we have, 4 other ways for teams.

Required number of ways = 210 × 4 = 840

shaalaa.com
Factorial N (N!) Permutations and Combinations
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 16: Permutations - Exercise 16.4 [पृष्ठ ३७]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 16 Permutations
Exercise 16.4 | Q 9 | पृष्ठ ३७

संबंधित प्रश्न

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


If (n + 2)! = 60 [(n − 1)!], find n. 


If (n + 3)! = 56 [(n + 1)!], find n.


If \[\frac{(2n)!}{3! (2n - 3)!}\]  and \[\frac{n!}{2! (n - 2)!}\]  are in the ratio 44 : 3, find n.

 

 


If P (n, 5) = 20. P(n, 3), find n ?


If P (9, r) = 3024, find r.


If P(11, r) = P (12, r − 1) find r.


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


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


In how many ways can five children stand in a queue?


From among the 36 teachers in a school, one principal and one vice-principal are to be appointed. In how many ways can this be done?


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 words, with or without meaning, can be formed by using all the letters of the word 'DELHI', using each letter exactly 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?


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


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

all vowels come together?


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

all consonants come together?


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:
INTERMEDIATE


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

RUSSIA


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


How many words can be formed by arranging the letters of the word 'MUMBAI' so that all M's come together?


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


How many different arrangements can be made by using all the letters in the word 'MATHEMATICS'. How many of them begin with C? How many of them begin with T?


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?


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?


If the letters of the word 'MOTHER' are written in all possible orders and these words are written out as in a dictionary, find the rank of the word 'MOTHER'.


In how many ways can the letters of the word
"INTERMEDIATE" be arranged so that:the vowels always occupy even places?


For all positive integers n, show that 2nCn + 2nCn − 1 = `1/2` 2n + 2Cn+1 


Evaluate

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

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

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

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


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×