मराठी

Convert the Following Products into Factorials: 3 · 6 · 9 · 12 · 15 · 18 - Mathematics

Advertisements
Advertisements

प्रश्न

Convert the following products into factorials: 

3 · 6 · 9 · 12 · 15 · 18

उत्तर

\[\ 3 \times 6 \times 9 \times 12 \times 15 \times 18 = \left( 3 \times 1 \right) \times \left( 3 \times 2 \right) \times \left( 3 \times 3 \right) \times \left( 3 \times 4 \right) \times \left( 3 \times 5 \right) \times \left( 3 \times 6 \right)\]
\[ = 3^6 \left( 1 \times 2 \times 3 \times 4 \times 5 \times 6 \right)\]
\[ = 3^6 \left( 6! \right)\]

shaalaa.com
Factorial N (N!) Permutations and Combinations
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 16: Permutations - Exercise 16.1 [पृष्ठ ४]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
पाठ 16 Permutations
Exercise 16.1 | Q 4.2 | पृष्ठ ४

संबंधित प्रश्‍न

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


If P (9, r) = 3024, find r.


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


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


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


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 the letters of the word 'TRIANGLE'?


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?


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?

 


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

the vowels occupy only the odd places?


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?


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?


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 at a time.


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


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


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 different signals can be made from 4 red, 2 white and 3 green flags by arranging all of them vertically on a flagstaff?


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 'LATE' be permuted and the words so formed be arranged as in a dictionary, find the rank of the word LATE.


If the permutations of a, b, c, d, e taken all together be written down in alphabetical order as in dictionary and numbered, find the rank of the permutation debac ?


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:

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

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 but first letter is a vowel?


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


Find the number of permutations of n different things taken r at a time such that two specified things occur together?


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


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


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×