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Byteland country is very famous for it's own variety of rules and customs. People from the normal world only knows 26 alphabets but the scientists in the Byteland country always try to invent new alphabets. Let N be the number of alphabets invented by the Byteland country scientists. Alice is living in Byteland country and one of her friends gifted her a new pet on her Birthday. In the Byteland country each pet must contain a name as suggested by the astronomer. After consulting an astronomer Alice came to know that length of the pet name must be of L letters and among L letters she need to keep X number of letter prefix as suggested by the astronomer. Now Alice has decided to form the names by following the astronomer's suggestion, as Alice is weak in mathematics can you please help her to find out the number of valid names that she can form

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TCS Other Question

The fig shows an equilateral triangle of side length 5,which is divided into unit triangle. a valid path is a path from d triangle in d top row to the middle triangle in the bottom row, such that adjacent triangles in our path share a common edge and d path never travels up (from a lower row to a higher row) or revisites a triangle. An example of one such path is illustrated below……

How many valid path are there?
a)23
b)16
c)120
d)24
I purchased 3 pens from a shop.I want to gift 5 pens to my sister in an order out of which i want to give 2 pens from those i purchased such that they occur as prefix in the order.
find how many combination of pen can i give..???