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permutation

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Source: — Problem Solving |
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by maihuna » Fri Feb 04, 2011 11:49 am
Its all about whether order matter or nat. You may pick any elementry book to see concepts.
Charged up again to beat the beast :)
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by one_pacifist » Fri Feb 04, 2011 9:49 pm
hi all

new to permutations and combinations topic, so need help on this ....

q) A set of 6 questions contains true /false type questions.
Maximum how many students can take the test if all the students answer differently from others and must attempt all the questions ?

a gud explanation on answer will help a lot!!!!!!
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by Night reader » Fri Feb 04, 2011 10:48 pm
one_pacifist wrote:hi all

new to permutations and combinations topic, so need help on this ....

q) A set of 6 questions contains true /false type questions.
Maximum how many students can take the test if all the students answer differently from others and must attempt all the questions ?

a gud explanation on answer will help a lot!!!!!!
Students can answer all 'True' --> 1
Students can answer all 'False' --> 1
Students can answer three 'True' the rest 'False' --> 6C3=6!/(3!*3!)=20
Students can answer four 'True' the rest 'False' --> 6C4=6!/(4!*2!)=15
Students can answer four 'False' the rest 'True' --> 6C4=6!/(4!*2!)=15
Students can answer five 'True' the rest 'False' --> 6C5=6!/(5!*1!)=6
Students can answer five 'False' the rest 'True' --> 6C5=6!/(5!*1!)=6

1+1+20+15+15+6+6=64 students can take the test if all the students answer differently from others and must attempt all the questions
Last edited by Night reader on Mon Feb 07, 2011 6:35 pm, edited 1 time in total.
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by one_pacifist » Sat Feb 05, 2011 2:29 am
@ night reader thanks man.. for your prompt reply... and the explanation.... keep in touch... :mrgreen: [/img]
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by 721tjm » Mon Feb 07, 2011 5:18 pm
I think this one might just be 2^6 = 64...

How many possible answers are there for the first question? 2
...second question? 2
and so forth

Multiply all the different scenarios together to equal 2*2*2*2*2*2 = 2^6 = 64

I think Night reader's on the right track but maybe double-counted a couple possibilities (the bold statements are the same scenario, the underlined are the same scenario, and the italics are the same scenario)

Students can answer all 'True' --> 1
Students can answer all 'False' --> 1
Students can answer two 'True' the rest 'False' --> 6C2=6*5/2=15
Students can answer two 'False' the rest 'True' --> 6C1=6*5/2=15
Students can answer three 'True' the rest 'False' --> 6C3=6!/(3!*3!)=20
Students can answer three 'False' the rest 'True' --> 6C3=6!/(3!*3!)=20
Students can answer four 'True' the rest 'False' --> 6C4=6!/(4!*2!)=15
Students can answer four 'False' the rest 'True' --> 6C4=6!/(4!*2!)=15
Students can answer five 'True' the rest 'False' --> 6C5=6!/(5!*1!)=6
Students can answer five 'False' the rest 'True' --> 6C5=6!/(5!*1!)=6
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by Night reader » Mon Feb 07, 2011 6:36 pm
thanks, I've over-counted/just edited my solution
I see your logic 6 ways to arrange each has 2 choices 2*2*...=2^6
721tjm wrote:I think this one might just be 2^6 = 64...

How many possible answers are there for the first question? 2
...second question? 2
and so forth

Multiply all the different scenarios together to equal 2*2*2*2*2*2 = 2^6 = 64

I think Night reader's on the right track but maybe double-counted a couple possibilities (the bold statements are the same scenario, the underlined are the same scenario, and the italics are the same scenario)

Students can answer all 'True' --> 1
Students can answer all 'False' --> 1
Students can answer two 'True' the rest 'False' --> 6C2=6*5/2=15
Students can answer two 'False' the rest 'True' --> 6C1=6*5/2=15
Students can answer three 'True' the rest 'False' --> 6C3=6!/(3!*3!)=20
Students can answer three 'False' the rest 'True' --> 6C3=6!/(3!*3!)=20
Students can answer four 'True' the rest 'False' --> 6C4=6!/(4!*2!)=15
Students can answer four 'False' the rest 'True' --> 6C4=6!/(4!*2!)=15
Students can answer five 'True' the rest 'False' --> 6C5=6!/(5!*1!)=6
Students can answer five 'False' the rest 'True' --> 6C5=6!/(5!*1!)=6
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