The formula used: The number of permutations of $n$ objects, where $p_{1}$ objects are of one kind, $p_{2}$ are of the second kind, …, $p_{k}$ is of a $k^{\text {th }}$ kind and the rest if any, are of a
Comments [ 5 ]
Rajan Biswas :
1 year ago
Anas Mohammed, the answer of your question is 12.
Rakshitha HM :
1 year ago
5!=5×4×3×2×1=120
PP repeated so 2!=2×1 =2
=5!÷2!
=60Amos Lalhmangaiha :
3 years ago
how that no.120 cames pliz explain??
Anas Mohammed :
3 years ago
How many permutation for the word Apple while the vowel occupy at even places?
Vengadesh Vicky :
4 years ago
Thank you so much
Complete step by step answer:
There are 5 letters in the word $\text{APPLE}$ out of which 2 are $P$’s and the rest are all distinct letters.
Here, we can use formula, \[\dfrac{{n!}}{{p!}}\]
Where $n$ is the total number of letters, and $p$ is the number of times a particular letter is repeated.
Permutations of the letters of the word APPLE =\[\dfrac{{5!}}{{2!}} = \dfrac{{5 \times 4 \times 3 \times 2 \times 1}}{{2 \times 1}} = 60\].
[Since, $5! = 5 \times 4 \times 3 \times 2 \times 1$ and $2! = 2 \times 1$]
Therefore, the permutations of the letters of the word APPLE are 60. So, the correct option is [C].
Note:
In these types of questions, first check whether a question is asked about combination or permutation. Permutation means arrangement of things, and combination means taking a particular number of items at a time [arrangement does not matter in combination]. Then apply the proper formula as required. Permutation means arrangement of letters. But be careful about repeated letters. If one, two or and any numbers of letters repeated, use the formula for the same. Also, if you get a factorial of the large number, never find the value of that factorial. Cancel the two factorials using proper rules. If in any case you get the final result in factorial of the large number, then leave the result in factorial form, don’t find the value.
Above are the words made by unscrambling N A M E S [AEMNS]. Our unscramble word finder was able to unscramble these letters using various methods to generate 62 words! Having a unscramble tool like ours under your belt will help you in ALL word scramble games!
How many words can you make out of NAMES?
To further help you, here are a few word lists related to the letters NAMES
N A M E S Letter Values in Word Scrabble and Words With Friends
Here are the values for the letters N A M E S in two of the most popular word scramble games.
Scrabble
The letters NAMES are worth 7 points in Scrabble
Words With Friends
The letters NAMES are worth 9 points in Words With Friends
If You Unscramble NAMES... What Does It Mean?
Definition of NAMES When Unscrambled
If we unscramble these letters, NAMES, it and makes several words. Here is one of the definitions for a word that uses all the unscrambled letters:
amens
More Information on the Letters NAMES
Unscrambling NAMES for Other Word Scramble Games
Scrambling the Letters in NAMES
According to our other word scramble maker, NAMES can be scrambled in many ways. The different ways a word can be scrambled is called "permutations" of the word.
According to Google, this is the definition of permutation:
a way, especially one of several possible variations, in which a set or number of things can be ordered or arranged.
How is this helpful? Well, it shows you the anagrams of names scrambled in different ways and helps you recognize the set of letters more easily. It will help you the next time these letters, N A M E S come up in a word scramble game.
NAEMS AENMS MNEAS MENAS NMEAS NMAES AMNES MANES ENAMS EMNAS NEAMS NEMAS EANMS ENMAS MNAES EMANS ANEMS ANMES