Using each letter of the word ZEBRA only once how many one, two, three

Question

Using each letter of the word ZEBRA only once how many one, two, three, four and five-letter words can be created ?

A. 20
B. 60
C. 100
D. 150
E. 325

From the word ZEBRA, how many different letter combinations can be arranged by using the foregoing letters?
A. 20
B. 60
C. 100
D. 120
E. 150

Dev23 · Answer

N= 5*4*3*2*1 + 5*4*3*2 + 5*4*3 + 5*4 + 5 = 325

stne · Answer

1  letter words :  5C1=5

2  letter words :  5C2∗2!=10

3  letter words :  5C3∗3!=60

4  letter words :  5C4∗4!=120

5  letter words :  5C5∗5!=120

Total  =5+10+60+120+120=325

Ans E

Hope it's clear.

ThatDudeKnows · Answer

How many 5-letter words? 5*4*3*2*1 = 120.
How many 4-letter words? 5*4*3*2 = 120.
That's already 240.

Answer choice E.

Emily1122 · Answer

Bunuel

Could you please help explain why we add?
It says "and", why do we add, not multiply?

Baxee · Answer

"And" does not necesserally means you multiply. Here, you have to find how many word of 1,2,3,4,5 letters you can do with the letters given. For 1 : 6 letters (Z E B R A) 
For 2 : 6 letters ( Z E B R A) and then 5, because you cannot use a letter you aleready used --> 6*5
 And so on until 6

pudu · Answer

single letter can taken in 5 ways.

Two letters can taken in 5C2*2!=20.
Three letters can taken in 5C3*3!=60
Four letters can taken in 5C4*4!=120
and five letters can taken in 5C5*5!=120

total=120+120+60=20+5=325

E

Its_me_aka_ak · Answer

why do we multiply 2! onto 5C2 and all?

stne · Answer

Hi  Its_me_aka_ak

5C2 is the number of ways to select 2 things from 5 things.

Note : Doing this does not consider different arrangements of the selected two things.

For e.g. = suppose we have A,B, C, D,E now how many ways to select two things out of 5 things ? This can be done in 5C2 ways. That's 10 ways.

AB
BC
DE 
AE
BE
CE
AC
AD
BD
CD

However in the given question since " words" need to be created hence AB and BA will be different words.

But doing 5C2 will not give AB and BA as two different words, it will only one word. To consider all the possibilities we need to multiply by the respective letters in the words.

In this question " Arrangement " also needs to be considered and not only selection.

Hence if we consider AB and BA as two arrangements then in total we will have 20 arrangements.

Hence we multiply by the respective number , because if word consists of two letters then number of ways to arrange them is 2!

If word consists of 3 letters then the number of ways to arrange them is 3!

Basically what we are doing is called permutation.

Hence we multiply by the number of alphabets in the words.

Note this is only in case all the alphabets are distinct, if alphabets are repeated then a different process needs to be followed.

you can visit the permuation and combination topic in gmat club and learn more about this.

Hope it helps.

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Using each letter of the word ZEBRA only once how many one, two, three

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Using each letter of the word ZEBRA only once how many one, two, three

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