In question 2 answer will be 52 (choosing worst-case scenario) = 10 blue + 8 green + 11 red + 11 yellow + 11 white + 1 (any) = 52 (this will have 12 balls of the same colour. )
Regarding the questions involving different color balls we did 5*11 this ensures that for each of the types of colored balls there are 11 balls present but that's not in the case of blue and green ....so I think the minimum numbers of balls will be 10 blue + 8 green + 11 of each red,yellow and white which makes it 51 and now if we add another of the white , red or yellow ball which are remaining we get 12 balls of same color so ans = 51+1 = 52. Plz clarify me if I am wrong.
6:14 in question 2 if we had to choose 12 balls of identical colors then there are no 12 balls of blue and green so we can't take 12 balls from each of either of the sets, in the worst case we can have 8 green, 10 blue, 11 red, 11 yellow, 11 black which still does not gurantee of having 12 identical balls but addition of 1 extra balls gurantees the same, so ans will be 8+10+(3*11)+1 = 52 balls
Last question right explaination:- so we have to allot 26 students 50 rooms at alternate positions , we have 25 alternate positions and students are 26 so 26/25 means atleast one room will contain ateast 2 students but it can't so we need an extra room but it can't be at alternate positions so 2 allotments atleast will be consicutive.
You are absolutely correct according to the principal but sometimes it is better to go with the estimation and in the Pigeon hole you can kind of take the next value and for me it works most of the time
Great Teacher! I just found your channel helpful in this course discrete mathematics. You teach us with examples and the concept is fastly cleared. on the other hand, many teachers take our hours and we spent but we don't undersatnd the concept. but you cleared this 1:30 lecture to 12: 00 and we thoroughly understood!
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Sir in question 2 there were only 10 blue balls and 8 green balls so they cannot be stacked up to 12 then there must be some other calculation to find a way around it
one correction to be made, it should be smallest integer function, since greatest integer will lesser than that number but vice versa for smallest integer function
Op sir Very helpful I count myself in those who enjoyed watching but never comment like subscribe We just come for getting knowledge here But now I am commenting because it act as a motivation for u sir
greatest integer function is also called floor function gives value of greatest integer that doesn't exceed x, the square brackets represent ceiling function here not floor function
pigeon hole is only applicable on red white and yellow balls because they are more than 12 in number rest we need to add the number of ball and boom we get our answer n=3 k+1=12---> k=11 also 10 blue + 8 green balls =18 kn+1= 11(3) +1 =34 now min number of balls = 18 +34 =52
pliz sir exaplain this Q.Suppose 14 students in a class appear at an examination. Prove that there exist atleast two among them whose seat numbers differ by a multiple of 13.
Sir your explanation of questions is right but the greatest integer function is incorrect for example the greatest integer of [3.5 ]= 3 not 4 and for [3.9] is also =4 There should be [m/n]+1 not [m/n] I prefer your video for greatest integer function and also searched about it
sir thoda students ke level ke acc. samjhaya karo kyuki aadho se jyada ka base clear ni hota ki sab advance me sikh jaaye turant..itna complex karke confuse kar diya
