Advertisements
Advertisements
प्रश्न
Convert the following products into factorials:
3 · 6 · 9 · 12 · 15 · 18
Advertisements
उत्तर
\[\ 3 \times 6 \times 9 \times 12 \times 15 \times 18 = \left( 3 \times 1 \right) \times \left( 3 \times 2 \right) \times \left( 3 \times 3 \right) \times \left( 3 \times 4 \right) \times \left( 3 \times 5 \right) \times \left( 3 \times 6 \right)\]
\[ = 3^6 \left( 1 \times 2 \times 3 \times 4 \times 5 \times 6 \right)\]
\[ = 3^6 \left( 6! \right)\]
APPEARS IN
संबंधित प्रश्न
Convert the following products into factorials:
1 · 3 · 5 · 7 · 9 ... (2n − 1)
Prove that: n! (n + 2) = n! + (n + 1)!
If (n + 1)! = 90 [(n − 1)!], find n.
Prove that:
If P (9, r) = 3024, find r.
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?
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 3-digit even number can be made using the digits 1, 2, 3, 4, 5, 6, 7, if no digits is repeated?
All the letters of the word 'EAMCOT' are arranged in different possible ways. Find the number of arrangements in which no two vowels are adjacent to each other.
How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:
the letter G always occupies the first place?
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 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?
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?
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 all letters are used but first is vowel.
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 '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 numbers can be formed with the digits 1, 2, 3, 4, 3, 2, 1 so that the odd digits always occupy the odd places?
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 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?
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 ways in which six ‘+’ and four ‘−’ signs can be arranged in a line such that no two ‘−’ signs occur together.
Evaluate
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 but first letter is a vowel?
How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?
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.
