Santosa, the question says she *may* choose to go barefoot. Hence there is an option, either she can wear one of her ten pairs of shoes or none of them, thus giving 11 options in all. Had it said she *will* go barefoot, then there would be only one option!
Avinash, suppose you got the first rank in History. Would that prevent you from also getting the first in Geography? The thing is that in this question, both “first ranks” can go to the same person. So whoever gets the top in Geography, there are ten people (including that person) who could get the first in History and hence 10 * 10. This is the basis on which most “repetition allowed” questions are based in fact.
Hello sir,In last question if we have question like 4 multiple questions with 5 choices each .In how many ways questions could be done if one must do at least 2 questions?
No we would also need to check which questions are answered in each case. So it would be 1 (0 questions) + 4C1*5 (1 question) + 4C2*25 (2 questions)and so on. Which would yield the same answer eventually, just more painfully!
CAT-holics 
in question 2,it was written barefoot, so with no pair of shoes i.e.1
how is this 11??
Santosa, the question says she *may* choose to go barefoot. Hence there is an option, either she can wear one of her ten pairs of shoes or none of them, thus giving 11 options in all. Had it said she *will* go barefoot, then there would be only one option!
J
ohh thank you…
btw ur articles r vry good & informative.
keep up d gd work…:)
the first rank in geography and first rank in history question, i didn’t understand. could you please elaborate?
Avinash, suppose you got the first rank in History. Would that prevent you from also getting the first in Geography? The thing is that in this question, both “first ranks” can go to the same person. So whoever gets the top in Geography, there are ten people (including that person) who could get the first in History and hence 10 * 10. This is the basis on which most “repetition allowed” questions are based in fact.
regards
J
Hello sir,In last question if we have question like 4 multiple questions with 5 choices each .In how many ways questions could be done if one must do at least 2 questions?
Pranita, then we would remove the cases where 0 or 1 question was answered. So 6^4 – 1 – 5*4 = 1296 – 21 = 1275 ways.
regards
J
sir, shouldn’t it be 5^4 – 1 – 5*4 = because attempting all questions in 5^4 ways?
No Seema, because each question still has the option of “not attempted” so 6 possibilities.
but it says, “at least 2 needs to be done” and in 6^4, if all were left unattempted, then?
That’s the first ( – 1) in the answer.
Why not all persons get first rank? The question doesn’t say only one should get first rank.
Long answer – when the question says “the first rank” then it is understood that there is only one first rank. Similarly for “the second rank.
Short answer “Bhavnaon ko samjho” 😛
regards
J
Could you tell your short answer in English.I don’t know Hindi
“Understand the intentions”. There’s this site called Google which would help in such cases, you know…try it sometime.
regards
J
Sir, in the last question, can;t it be she attempts 0 ques or 1 ques or 2 ques and so on. 5(for 1ques)+ 25(for 2) +125+625
No we would also need to check which questions are answered in each case. So it would be 1 (0 questions) + 4C1*5 (1 question) + 4C2*25 (2 questions)and so on. Which would yield the same answer eventually, just more painfully!
regards
J
Glad I found your blog, will be revising all concepts from here in the remaining days 😀