QR question from topscore - need help

[buchey]

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this is question #9 from test 1 on topscore, that i find impossible without a calculator....

what is the probability of six tails out of nine tosses of a fair coin?

the solution shows the formula (nCr)(p^r)(q^(n-r))
nCr=(9*8*7*6*5*4)/(6*5*4*3*2*1)=84
(1/2)^6=1/16
(1/2)^3=1/8
84*(1/8)(1/64)=21/128

the answer is 21/128, but the solution method in topscore would be near impossible without a calculator! any suggestions how to do this quickly, or am i missing an obvious strategy??
thanks for any help

 

[joonkimdds]

this is question #9 from test 1 on topscore, that i find impossible without a calculator....

what is the probability of six tails out of nine tosses of a fair coin?

the solution shows the formula (nCr)(p^r)(q^(n-r))
nCr=(9*8*7*6*5*4)/(6*5*4*3*2*1)=84
(1/2)^6=1/16
(1/2)^3=1/8
84*(1/8)(1/64)=21/128

the answer is 21/128, but the solution method in topscore would be near impossible without a calculator! any suggestions how to do this quickly, or am i missing an obvious strategy??
thanks for any help

U don't need calculator, nor ur brain. Just write them on a paper and multiply, it's algebra1 level of multiplication i should say. Even though it's taking about 3 min.

 

[paulee1983]

U don't need calculator, nor ur brain. Just write them on a paper and multiply, it's algebra1 level of multiplication i should say. Even though it's taking about 3 min.

Maybe I am dumb
but there are 2 possible outcomes for each toss
for nine tosses there should be (1/2^9) = 512 outcomes
and we need 6 of them being tails
so isn't that the answer is 6/512 = 3/256?
Or am I missing something? 🙁

 

[Richnator]

First of all, I heard those complicated questions usually never occur in the real DAT. However, the trick is to cancel out common factors.

 

[seoul]

this is question #9 from test 1 on topscore, that i find impossible without a calculator....

what is the probability of six tails out of nine tosses of a fair coin?

the solution shows the formula (nCr)(p^r)(q^(n-r))
nCr=(9*8*7*6*5*4)/(6*5*4*3*2*1)=84
(1/2)^6=1/16
(1/2)^3=1/8
84*(1/8)(1/64)=21/128

the answer is 21/128, but the solution method in topscore would be near impossible without a calculator! any suggestions how to do this quickly, or am i missing an obvious strategy??
thanks for any help

Someone's asked a similar question from Barron, and the following is how I would suggest:

There're 9! way of arranging the 9 tosses in a straight row, and out of these 6 tails look alike, while the other 3 heads appear identical, leading to a permutation of:

9!(6!3!) ---- (1)

Multiplication rule applies when you have 9 tosses in a row, leading to a total number of appearances:

2^9 ----- (2)

The probability of getting 6 tails out of nine tosses is therefore:

P👎 = [9!(6!3!)]/(2^9) = (9 X 8 x 7)/(3 x 2 X 2^3 x 2^6) = 21/128

All in all shouldn't be taking you more than a minute to get the problem solved.