On the third day of Christmas, Calvin gave to me

3 French Hens

The french translation of “Hens” is “Poules”. How many different ways are there to rearrange all the letters in “Poules”?


The answer is 720.

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

26 solutions

Ajay Maity
Dec 23, 2013

As a simple rule, just remember any word with n n distinct letters can be rearranged in n ! n! ways.

Here "Poules" have all distinct characters, so the number of rearrangements are equal to 6 ! = 720 6! = 720 .

If, consider the situation where the letters are repeated. Suppose, we have "Popoulleso". Here, the number of rearrangements would be 10 ! 2 ! × 3 ! × 2 ! \frac{10!}{2! \times 3! \times 2!} . The denominator terms refer to the number of repetitions of each letters - 'p' and 'l' are repeated twice and 'o' is repeated thrice. Ofcourse, that wouldn't help in this question. I just wrote it as a side note for someone who doesn't confuse it with a word having repeated letters.

Very easy. Just do 6!

Anuj Shikarkhane - 6 years, 11 months ago
Noonoo Wang
Dec 22, 2013

There are 6 ways for the first, 5 for the second, .... and 1 for the last. 6!=720.

Puja Shree
Dec 24, 2013

there are 6 letters . so to rearrange them there are 6! ways = 6x5x4x3x2x1= 720 there fore 720 ways to rearrange " Poules "

Ameya Salankar
Dec 24, 2013

There are 6 letters in the word 'poules'. Hence to there are 6! = 720 different ways of arranging the letters.

Krishna Karthik
Nov 19, 2018

6! = 720

Lulu Cajica
May 20, 2016

"Poules" have 6 letters, so all the posible ways that the word can be rearranged are 6! = 720.

It's simple The fact of the answer is 6! 6×5×4×3×2×1 = 720

Aashish Patel
Apr 16, 2014

It is quite simple.Always the ways of rearrangement of letters in a word is the facorial of number of letters in the word.Hence,here it is number of letters is 6.So the factorial of 6 is 720.Thus the letters of the word could be rearranged in 720 ways.

Philippe Arnoux
Mar 27, 2014

6 ! = 720 solutions.

Nitin Kumar
Mar 13, 2014

POULES have 6 distinct characters . so total no. of rearrangements are 6! = 720 . as each character can be used only once.

There are 6 unique letters in the word POULES which can be arranged in 6 ! ways = 720.

Abdul Lah
Mar 12, 2014

since the word "poules"consist of 6 letters and no letter is repeated so different number of ways is 6! = 6 5 4 3 2*1 = 720

Meldrin Rebello
Mar 9, 2014

7!

Victor Loh
Jan 3, 2014

There are 6 6 different letters in the word 'Poules', hence the number of ways to rearrange the letters is 6 ! = 720 6! = \boxed{720} .

Isaac Jacobs
Dec 31, 2013

since there are no repeats allowed the largest amount of combinations is 6!, or 720

Hibah Mirza
Dec 26, 2013

Simple; take out the factorial of 6, which is the number of letters in the word. Factorial of 6 = 6 x 5 x 4 x 3 x 2 x 1 = 720

Ansh Sharma
Dec 26, 2013

Number of letters (alphabets) in the word P o u l e s 'Poules' are 7 7 , therefore the number of possible combinations are 7 ! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 720 7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = \boxed{720}

Really sorry made a mistake, the number of letters are actually 6 6 , so it comes as 6 ! = 6 × 5 × 4 × 3 × 2 × 1 = 720 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = \boxed{720} .

Ansh Sharma - 7 years, 5 months ago
Prasun Biswas
Dec 25, 2013

In the word 'Poules', there are 6 distinct letters and these letters can be rearranged by permuting the 6 letters taken all at a time. So, the letters can be rearranged in = 6 P 6 = 6 ! = 720 =6P6 = 6! = \boxed{720} ways.

So, total no. of ways(rearrangements for the word) = 720 =\boxed{720}

Charlie Wilkinson
Dec 25, 2013

Very simply, a way to find how many ways to arrange n objects is n!, or n factorial. 6! is 6 * 5 * 4 * 3 * 2 * 1 = 720. Therefore: You can arrange the 6 letters in poules in 720 ways. This amazing numberphile video includes a bit more about factorials, particularly 0! http://www.numberphile.com/videos/zero_factorial.html

Tushar Ranjan
Dec 25, 2013

There are 6 alphabets in the word Poules so, 6! = 6 5 4 3 2*1 =720

Iqra Noor
Dec 24, 2013

POULES has 6 words so there are 6 factorial ways to rearrange this word so 6 5 4 3 2*1=720 ways

6!=720

Iqra Noor - 7 years, 5 months ago
Nishant Singh
Dec 24, 2013

ther are 6 letters in "poules" , s0 ways of arrangment= 6!= 720

Rizky Riman
Dec 24, 2013

There's 6 alphabet and no alphabet is repeated. So, it's 6!

Nimesh Patodi
Dec 22, 2013

Number of ways of rearranging a "n" letter word which has no repeated letter=n! Hence, number of ways of arranging poules(6-letters) = 6! = 720

6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

Gaurang Pansare
Dec 22, 2013

Since there are six distinct letters in "POULES",

the total number of ways to rearrange them is 6 ! 6!

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...