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# When six fair coins are tossed simultaneously, in how many of the outc

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Math Expert
Joined: 02 Sep 2009
Posts: 53020
When six fair coins are tossed simultaneously, in how many of the outc  [#permalink]

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29 Jan 2019, 06:54
00:00

Difficulty:

65% (hard)

Question Stats:

32% (02:24) correct 68% (02:12) wrong based on 21 sessions

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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. 22

B. 31

C. 32

D. 41

E. 42

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Joined: 29 Jan 2019
Posts: 1
Re: When six fair coins are tossed simultaneously, in how many of the outc  [#permalink]

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29 Jan 2019, 07:53
64 total outcomes (2^6).

0H6T - 1 possible outcome
1H5T - 6 possible outcomes
2H4T - 15 possible outcomes (5+4+3+2+1)
3H3T - screw figuring it out, it has to be symmetrical with tails anyway so I'll come back to it

4H2T - 15 outcomes
5H1T - 6 outcomes
6H0T - 1 outcome

3H3T = 64 - (15+6+1) - (15+6+1) = 20

1+6+15+20 = 42.

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Re: When six fair coins are tossed simultaneously, in how many of the outc  [#permalink]

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29 Jan 2019, 09:07
Bunuel wrote:
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. 22

B. 31

C. 32

D. 41

E. 42

at most 3 means ; to the max 3
we will have 4 cases:
case1 ; flip coin 6 times we get 0 H and 6 T ; 6c0
case2: 1 H and 5 T ; 6c1
case3 ; 2 H and 4 T= 6c2
case 4 : 3 H and 3 T = 6c3

so total outcomes to get H at most 3 times
6c0+6c1+6c2+6c3 = 1+6+15+20 = 42
IMO E
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Re: When six fair coins are tossed simultaneously, in how many of the outc  [#permalink]

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01 Feb 2019, 07:06
Bunuel wrote:
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. 22

B. 31

C. 32

D. 41

E. 42

= 6C0 + 6C1 + 6C2 + 6C3

= 1 + 6 + (6 x 5)/2 + (6 x 5 x 4)/(3 x 2)

= 1 + 6 + 15 + 20

= 42

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Re: When six fair coins are tossed simultaneously, in how many of the outc   [#permalink] 01 Feb 2019, 07:06
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