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3 years ago

in how many different ways can t e letters of the word "LEADING" be arranged in such a way that vowels always come together?

2 answers:

5 0

The word 'LEADING' has 7 different letters. When the vowels EAI are always together, they can be supposed to form one letter. Then, we have to arrange the letters LNDG (EAI). Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways. The vowels (EAI) can be arranged among themselves in 3! = 6 ways. <span> Required number of ways = (120 x 6) = 720. The word 'LEADING' can be arranged 720 different ways in such a way that vowels always come together. </span>

soldi70 [24.7K]3 years ago

5 0

We have 3 vowels. The number of ways we can arrange them so they are next to each other is 3!=6. Now we have to find the number of ways we can arrange these 3 vowels with the remaining letters. As the vowels have to come together, we can treat them as one letter. Therefore we have 5 letter altogether. The number of ways we can arrange the vowels with the remaining letters is 5!=120.

6*120=720

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2 years ago

Graphing inequality's

Pani-rosa [81]

Answer :

$\boxed{\textsf {The red area is the required answer . }}$

Step-by-step explanation:

A linear inequality in two variables is given to us and we need to plot it's graph .So the the given inequality is ,

$\sf\implies y \geq- \dfrac{1}{5}x +5$

So firstly let's simplify out the inequality for easy plotting of the graph .

$\sf\implies y \geq- \dfrac{1}{5}x +5 \\\\\sf\implies y \geq \dfrac{-x+5(-5)}{5}\\\\\sf\implies y \geq \dfrac{-x-25}{5}\\\\\sf\implies y \geq -(1)\dfrac{x+25}{5}$

Now let's put some values of x to get values of y .

• Firstly put x = 0 then we get , y is greater than or equal to 0+5/5 (-1) = 5/5(-1) = -1 . Hence we get y ≥ (-1) .

• Secondly put x = 1 , then we get , y is greater than or equal to 1+5/5(-1)=6/5(-1) = -6/5 . Hence we get y ≥ -6/5 .

• Thirdly put x = -1 , then we get y is greater than or equal to -1+5/5(-1) = -4/5 . Hence we get y ≥ -4/5

• Fourthly put x = (-5) , then we get y is greater than or equal to -5+5/5(-1) = 0 .Hence we get y ≥ 0 .

With reference to these let's plot a graph . For the graph kindly refer to the attachment :) .

Here in the graph the red area shows the possible values of x and y .

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