Advertisements
Advertisements
Question
Convert the following products into factorials:
3 · 6 · 9 · 12 · 15 · 18
Advertisements
Solution
\[\ 3 \times 6 \times 9 \times 12 \times 15 \times 18 = \left( 3 \times 1 \right) \times \left( 3 \times 2 \right) \times \left( 3 \times 3 \right) \times \left( 3 \times 4 \right) \times \left( 3 \times 5 \right) \times \left( 3 \times 6 \right)\]
\[ = 3^6 \left( 1 \times 2 \times 3 \times 4 \times 5 \times 6 \right)\]
\[ = 3^6 \left( 6! \right)\]
APPEARS IN
RELATED QUESTIONS
Convert the following products into factorials:
5 · 6 · 7 · 8 · 9 · 10
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.
If P(11, r) = P (12, r − 1) find r.
If P (n, 4) = 12 . P (n, 2), find n.
Prove that:1 . P (1, 1) + 2 . P (2, 2) + 3 . P (3, 3) + ... + n . P (n, n) = P (n + 1, n + 1) − 1.
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?
How many words, with or without meaning, can be formed by using the letters of the word 'TRIANGLE'?
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 with the letters of word 'SUNDAY'? How many of the words begin with N? How many begin with N and end in Y?
How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:
the letters P and I respectively occupy first and last place?
How many permutations can be formed by the letters of the word, 'VOWELS', when
there is no restriction on letters?
How many permutations can be formed by the letters of the word, 'VOWELS', when
all vowels come together?
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:
CONSTANTINOPLE
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 number of four digits can be formed with the digits 1, 3, 3, 0?
In how many ways can the letters of the word 'ARRANGE' be arranged so that the two R's are never together?
How many different numbers, greater than 50000 can be formed with the digits 0, 1, 1, 5, 9.
How many permutations of the letters of the word 'MADHUBANI' do not begin with M but end with I?
Find the total number of permutations of the letters of the word 'INSTITUTE'.
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'.
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.
Evaluate
Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
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 different things taken r at a time such that two specified things occur together?
Write the expression nCr +1 + nCr − 1 + 2 × nCr in the simplest form.
Write the number of ways in which 12 boys may be divided into three groups of 4 boys each.
Write the total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants.
