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# From the set of numbers x, y, t, z and w, how many different

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Intern
Joined: 05 Jun 2010
Posts: 3
From the set of numbers x, y, t, z and w, how many different  [#permalink]

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19 Jun 2010, 15:48
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Difficulty:

55% (hard)

Question Stats:

59% (01:44) correct 41% (02:02) wrong based on 110 sessions

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From the set of numbers x, y, t, z and w, how many different combinations can we have without the t in them? Ex:. (x,y), (x), (w,z,y,x), etc and (x,y)=(y,x)

A. 10
B. 14
C. 15
D. 16
E. 30
Math Expert
Joined: 02 Sep 2009
Posts: 56261

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19 Jun 2010, 15:59
2
Gusano97 wrote:
Could anybody help me with these problem?

From the set of numbers x, y, t, z and w, how many different combinations can we have without the t in them? Ex:. (x,y), (x), (w,z,y,x), etc and (x,y)=(y,x)

A)10
B)14
C)15
D)16
E)30

There are 4 letter without t: x, y, z, and w, so:
$$C^1_4+C^2_4+C^3_4+C^4_4=4+6+4+1=15$$

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22 Jun 2010, 15:23
2
1
Another way: Any letter (x, y, z, w) can be included or not. So, we have 2^4 combinations - 1 empty combination = 15 combinations
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Manager
Joined: 22 May 2015
Posts: 123
Re: From the set of numbers x, y, t, z and w, how many different  [#permalink]

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10 Apr 2017, 17:09
Question is to find no of combinations of x,y,z,w

Choosing only 1 letter - 4C1 ways = 4
Choosing only 2 letter - 4C2 ways = 6
Choosing only 3 letter - 4C3 ways = 4
Choosing only 4 letter - 4C4 ways = 1

Total possible combinations = 4+6+4+1 = 15
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Joined: 18 Jun 2018
Posts: 267
Re: From the set of numbers x, y, t, z and w, how many different  [#permalink]

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18 Aug 2018, 10:56
Gusano97 wrote:
From the set of numbers x, y, t, z and w, how many different combinations can we have without the t in them? Ex:. (x,y), (x), (w,z,y,x), etc and (x,y)=(y,x)

A. 10
B. 14
C. 15
D. 16
E. 30

OA:C
Set of numbers formed by using x, y,z and w
Case 1 : Using 1 number only
C(4,1) =4
Case 2 : Using 2 number only
C(4,2) =6
Case 3 : Using 3 number only
C(4,3) =4
Case 4 : Using 4 number only
C(4,4) =1
Total cases :4+6+4+1=15
Re: From the set of numbers x, y, t, z and w, how many different   [#permalink] 18 Aug 2018, 10:56
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