Q1- There are six stair step on a stair case. Issac can take a single, double or triple step at a time. How many ways are there to climb up the whole stair case. For example issac first takes a single step, then three steps at once then a single step again. This is one possible way to climb the stair case. Give all the possibilities of Issac climbing the stairs. See in the diagram that triple step is not shown. Use your imagination Issac jumps to take three steps at once.
p.s; Sorry for the bad drawing ^_^

Q2- Faraday is a mad scientist who has a lot of time on his hands. One day he was looking at his simple calculator (see diagram below). He thought to himself, “How many ways can I do addition if at least 4 digit numbers are used”. You have to think of the possibilities! For example one way is 1+1 , second way is 1+2 third way is 1+3 fourth way can be 9999+9999 (this is the maximum values you can use). (Optional Question Only solve if you have solved other questions and think you are right about them)
Q3- From a group of 15 people only 10 people are selected in an International Gaming event. The group has 8 boys and 7 girls. The gaming event contains 2 different games. First one is Counter strike in which 2 girls are must. The counter strike team consists of 5 players. The Second one is Dota 2 in which 3 boys must be selected. The team consists of 5 players. Give the number of possibilities in how many ways the team of 10 people from 15 people can be selected.

Q4-In how many ways can the word ACHIEVEMENT be arranged in such a way that the vowels always come together.

Q5-How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?

Q6- There are three different boxes on a shelf. First box has a capacity of filling 3 toys, second box has a capacity of 5 toys and third one has 2 toys. Timmy is growing up and now needs to donate the toys to a small nursery. Timmy has 6 favourite toys (only favourite toys meaning he has more toys) he wants to give to the nursery
(a) How many ways are there to pack them in the 3 boxes.
(b) Suppose timmy has 15 red toys, 10 yellow toys and 5 green ones. He only wants to give 3 red, 5 yello and 2 green ones. How many possible ways can he give the toys to the nursery in the three boxes.

Q7- 5 boys and 4 girls have to stand in a line such that no two girls are next to each other. How many possible ways ?

The quiz is open book and open to internet. It is recommended that you first try the questions yourself. If you want to search for answers your most welcome. You have till Sunday mid night. Happy hunting