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प्रश्न
Convert the following products into factorials:
3 · 6 · 9 · 12 · 15 · 18
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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:
(n + 1) (n + 2) (n + 3) ... (2n)
Prove that: n! (n + 2) = n! + (n + 1)!
Prove that:
\[\frac{n!}{(n - r)! r!} + \frac{n!}{(n - r + 1)! (r - 1)!} = \frac{(n + 1)!}{r! (n - r + 1)!}\]
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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
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How many permutations can be formed by the letters of the word, 'VOWELS', when
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EXERCISES
A biologist studying the genetic code is interested to know the number of possible arrangements of 12 molecules in a chain. The chain contains 4 different molecules represented by the initials A (for Adenine), C (for Cytosine), G (for Guanine) and T (for Thymine) and 3 molecules of each kind. How many different such arrangements are possible?
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?
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 ?
In how many ways can the letters of the word
"INTERMEDIATE" be arranged so that:the vowels always occupy even places?
Evaluate
Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
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 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?
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.
