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CBSE Class 12-science Answered

The numbers 1,2,3, .. , n are arranged in a random order. The probability that the digits 1,2,3,..,k appear as neighbour is ?
Asked by Paavani | 26 Dec, 2015, 10:51: AM
answered-by-expert Expert Answer
bold Total bold space bold number bold space bold of bold space bold ways bold space bold of bold space bold arranging bold space bold apostrophe bold n bold apostrophe bold space bold distinct bold space bold numbers bold equals bold n bold factorial bold. bold. bold. bold. bold. bold left parenthesis bold 1 bold right parenthesis bold If bold space bold apostrophe bold k bold apostrophe bold space bold of bold space bold these bold space bold numbers bold space bold are bold space bold neighbours bold space bold always bold comma bold space bold we bold space bold can bold space bold consider bold space bold these bold space bold apostrophe bold k bold apostrophe bold space bold things bold space bold as bold space bold one bold space bold unit bold. stack bold 1 bold comma bold space bold 2 bold comma bold space bold 3 bold comma bold. bold. bold. bold. bold comma bold space bold k with bold underbrace below bold comma bold space bold k bold plus bold 1 bold comma bold space bold K bold plus bold 2 bold comma bold. bold. bold. bold comma bold space bold n bold So bold space bold effectively bold space bold we bold space bold are bold space bold making bold space bold arrangement bold space bold of bold space bold n bold minus bold k bold plus bold 1 bold space bold numbers bold. bold Total bold space bold number bold space bold of bold space bold arrangement bold space bold possible bold space bold for bold space bold this bold space bold is bold space open parentheses bold n bold minus bold k bold plus bold 1 close parentheses bold factorial bold apostrophe bold k bold apostrophe bold space bold things bold space bold can bold space bold also bold space bold be bold space bold arranged bold space bold among bold space bold themselves bold space bold in bold space bold k bold factorial bold space bold ways bold. bold So bold comma bold space bold favorable bold space bold number bold space bold of bold space bold ways bold equals open parentheses bold n bold minus bold k bold plus bold 1 close parentheses bold factorial bold cross times bold k bold factorial bold So bold space bold probability bold space bold equals bold space fraction numerator open parentheses bold n bold minus bold k bold plus bold 1 close parentheses bold factorial bold cross times bold k bold factorial over denominator bold n bold factorial end fraction
Answered by satyajit samal | 28 Dec, 2015, 04:59: PM

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CBSE 12-science - Maths
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Asked by armaanjain840 | 20 Dec, 2023, 05:59: PM
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CBSE 12-science - Maths
A bag contains 5 white balls and 9 red balls. Three balls are drawn from the bag. What is the probability that at least one ball is white?: Looks like answer posted as 55/182 is wrong. Request to recheck it once again.
Asked by sachinkumarmishra1 | 31 Jan, 2020, 05:17: PM
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CBSE 12-science - Maths
A bag contains 5 white balls and 9 red balls. Three balls are drawn from the bag. What is the probability that at least one ball is white?
Asked by sachinkumarmishra1 | 29 Jan, 2020, 02:59: PM
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CBSE 12-science - Maths
A bag contains 5 white balls and 9 red balls. Three balls are drawn, without replacement, from the bag. What is the probability that at least one ball is white?
Asked by sachinkumarmishra1 | 27 Jan, 2020, 12:27: PM
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CBSE 12-science - Maths
A bag contains 7 white , 5 Black and 4 red balls. 4 balls are drawn without replacement. Find the probability that atleast 3 balls are black.
Asked by sachinkumarmishra1 | 24 Jan, 2020, 11:10: AM
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CBSE 12-science - Maths
From a bag containing 8 white and 5 Black balls. Four balls are drawn one by one without replacement . Find the probability that exactly two of them are white.
Asked by sachinkumarmishra1 | 23 Jan, 2020, 12:00: PM
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CBSE 12-science - Maths
a bag contains 4 red ,6 green, 3 white balls ,three balls are drawn one after one the other without replacement,find the probability that the balls are red,green and green  My doubt is --How can we solve this question by combination ? The explanation given is    begin mathsize 16px style probability space of space taking space 1 st space ball space red space ball equals 4 over 13 probability space of space taking space 2 nd space ball space green space ball equals 6 over 12 space left parenthesis no space replacement right parenthesis probability space of space taking space 3 rd space ball space green space ball equals 5 over 11 space left parenthesis no space replacement right parenthesis so space in space total 4 over 13 cross times 6 over 12 cross times 5 over 11 end style  
Asked by sachinkumarmishra1 | 22 Jan, 2020, 05:50: PM
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CBSE 12-science - Maths
Neelam has offered physics , chemistry and mathematic sin class XII. She estimates that her probabilities of receiving a grade A  in these course are 0.2 , 0.3 and 0.9  respectively . Fins the probability that neelam receives : exactly 2A grades
Asked by haroonrashidgkp | 05 Nov, 2018, 02:11: PM
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CBSE 12-science - Maths
What are independent events? 
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
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CBSE 12-science - Maths
If A and B are independent events, such that P(A) = , P(B) = , then find .       
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
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