हिंदी

Write the Number of Parallelograms that Can Be Formed from a Set of Four Parallel Lines Intersecting Another Set of Three Parallel Lines.

Advertisements
Advertisements

प्रश्न

Write the number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines.

Advertisements

उत्तर

A parallelogram is formed by choosing two straight lines from a set of four parallel lines and two straight lines from a set of three parallel lines.
Two straight lines from the set of four parallel lines can be chosen in 4C2 ways and two straight lines from the set of three parallel lines can be chosen in 3C2 ways.
∴ Number of parallelograms that can be formed =

\[\ ^{4}{}{C}_2 \times \ ^{3}{}{C}_2 = \frac{4!}{2! 2!} \times \frac{3!}{2! 1!} = 6 \times 3 = 18\]

 

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 8 | पृष्ठ २४

संबंधित प्रश्न

Convert the following products into factorials:

5 · 6 · 7 · 8 · 9 · 10


Convert the following products into factorials:

1 · 3 · 5 · 7 · 9 ... (2n − 1)


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


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: 

\[\frac{n!}{(n - r)!}\] = n (n − 1) (n − 2) ... (n − (r − 1))

Prove that:

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

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


If nP4 = 360, find the value of n.


If P (n − 1, 3) : P (n, 4) = 1 : 9, find n.


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?


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 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 come together?

 


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\[\frac{m! (m + 1)!}{(m - n + 1) !}\]


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:
EXERCISES


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?


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


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?


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)!


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


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 at a time 


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


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


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.


Write the total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×