Once again, we return to the ice cream shop. I want an ice cream cone (no froze

Question

Once again, we return to the ice cream shop. I want an ice cream cone (no froze or sorbet): I get a cone with 3 scoops, each a different flavor. How many choices do I have if I only care which flavors are scooped and not their order? I get a cone with 3 scoops, each a different flavor. How many choices do I have if I care the order in which the flavors are scooped? I get a cone with 3 scoops, containing 2 flavors (so I'll have 2 scoops of one flavor and 1 scoop of the other). How many choices do I have if I only care how much of each flavor we have? I get a cone with 3 scoops, containing 2 flavors (so I'll have 2 scoops of one flavor and 1 scoop of the other). How many choices do I have if I care the order m which flavors are scooped? I decide to have a different flavor of ice cream each day for a week. I try chocolate ice cream the day alter I try vanilla ice cream. How many assortments can I try this week? For instance: strawberry and then mint Ana then vanilla and then chocolate and then Oreo and then banana and then rocky road. I change my mind and want one scoop of a sorbet this week. Repeat the previous question, but with exactly one scoop of sorbet this week (still have chocolate the day after vanilla). I have a standard 52 card deck (with 4 suits containing 13 cards each). I choose a 5 card hand (a 'hand' contains 5 cards with no particular order). How many hands contain 3 Queens and 2 Sevens? How many hands contain at least 1 Queen? Count by complement. How many hands contain at least 2 Queens?

Explanation / Answer

Soution of Question no2:-

Part 1

You have asked About No.of hands with 3 Queen and 2 seven

Total no of queen =4   total number of seven =4

Total choice =4C3*4C2 =4*6=24

Part 2:

Aleast one Queen mean Queen may be 1,2,3,4 So total order=

Atleast one Queen = 4C1*48C4+4C2*48C3+4C3*48C2+4C4*48C1=4*194580 +6*17296 +4*1128 +1*48=778320+103776+4512+48=886656

Atleast two Queen mean Queen may be 2,3,4 so total order =

Atleast two Queen =4C2*48C3+4C3*48C2+4C4*48C1=108336

Solution of Question No.1:

Part 1: you have 3 scoops .Let scoop is A,B,C,

(repetation is not allowed here)

you may number of choice=3C1=3

Part 2: If order matter than possible orders are ..

(repetation is not allowed here)

(ABC,ACB,BAC,BCA,CAB,CBA)

Total =6

Part 3 : only two way (f1,f2) (f2,f1)

Part 4: possible order=(ABB,BAB,BBA)=3

Part 5: we have to take 7 type of ice cream and possible orders are = 7*6*5*4*3*2*1=5040

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