Permutation-Combination
Aptitude

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Q.

When six fair coins are tossed simultaneously, in how many of the outcomes will at most three of the coins turn up as heads?

 A.

$2^5$

 B.

$41$

 C.

$22$

 D.

$42$

 E.

$31$

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Solution:
Option(D) is correct

The question requires you to find a number of the outcomes in which at most $3$ coins turn up as heads.

i.e., $0$ coins turn heads or $1$ coin turns head or $2$ coins turn heads or $3$ coins turn heads.

The number of outcomes in which $0$ coins turn heads is ${^6C_0} = 1$ outcome

The number of outcomes in which $1$ coin turns head is ${^6C_1} = 6$ outcomes

The number of outcomes in which $2$ coins turn heads is ${^6C_2} = 15$ outcomes

The number of outcomes in which $3$ coins turn heads is ${^6C_3} = 20$ outcomes.

Therefore, total number of outcomes,

$= 1 + 6 + 15 + 20$

$= 42\text{ outcomes.}$

Edit: Corrected the typo after it was pointed by Kiran.


(1) Comment(s)


Kiran
 ()

The number of outcomes in which 3 coins turn heads is $^6C_0=20$ outcomes.

where $^6C_0$ is $^6C_3