A bag contains indentical balls of different colours.There are 12 red, 10 white, 8 yellow, 3 blue and 2 black balls.Without looking into the bag,John takes out the balls one by one.What is the least number of balls that John must take out from the bag in order to have at least 4 balls of the same colour?
3. Students in a primary school are either wearing blue, black or yellow cap. At least how many students are there to ensure there are 26 students wearing the same colour of cap?
there are 27 blue,12 yellow and 42 black marbles in a box.Jack close his eyes and draw a marble from the box.at least how many marble must be put out ensure that there are six ball of the same colour
Combinatorics
21. 15 students join a competition. Only top 5 students can be promoted to next round. How many different way(s) of promotion advance is / are there?
Different way: Cách khác nhau.
22. It is known that there are 8 classes of grade 5 in a primary school. At least how many students are there in grade 5 to ensure there exist 41 students in the same class?
At least: Ít nhất; Ensure: Chắc chắn; Exist: Tồn tại.
23. Choose 3 digits from 1, 2, 3, 4, 6, 8 and 0 to form 3-digit numbers. How many even number(s) greater than 300 is / are there? (The repetition of digits is not allowed)
Digit: Chữ số; 3-digit number: Số có 3 chữ số; Even number: Số chẵn; Greater than: Lớn hơn; Repetition of digits is not allowed: Các chữ số không được lặp lại.
24. A flight of stairs has 10 steps. Peter can go up for 1 step, 2 steps or 3 steps each time. How many way(s) is / are there for Peter to go up the stairs?
Step: Bước; Way: Cách.
25. Numbers are drawn from 80 integers 20 to 99. At least how many number(s) is / are drawn at random to ensure that there are two numbers whose sum is 85?
Integer: Số nguyên; At least: Ít nhất; Random: Ngẫu nhiên; Ensure: Chắc chắn; Sum: Tổng.
~ End of Paper ~
Combinatorics
21. 15 students join a competition. Only top 5 students can be promoted to next round. How many different way(s) of promotion advance is / are there?
Different way: Cách khác nhau.
22. It is known that there are 8 classes of grade 5 in a primary school. At least how many students are there in grade 5 to ensure there exist 41 students in the same class?
At least: Ít nhất; Ensure: Chắc chắn; Exist: Tồn tại.
23. Choose 3 digits from 1, 2, 3, 4, 6, 8 and 0 to form 3-digit numbers. How many even number(s) greater than 300 is / are there? (The repetition of digits is not allowed)
Digit: Chữ số; 3-digit number: Số có 3 chữ số; Even number: Số chẵn; Greater than: Lớn hơn; Repetition of digits is not allowed: Các chữ số không được lặp lại.
24. A flight of stairs has 10 steps. Peter can go up for 1 step, 2 steps or 3 steps each time. How many way(s) is / are there for Peter to go up the stairs?
Step: Bước; Way: Cách.
25. Numbers are drawn from 80 integers 20 to 99. At least how many number(s) is / are drawn at random to ensure that there are two numbers whose sum is 85?
Integer: Số nguyên; At least: Ít nhất; Random: Ngẫu nhiên; Ensure: Chắc chắn; Sum: Tổng.
~ End of Paper ~
There are 3 grey socks, 3 blue socks and 3 yellow socks in a drawer. How many socks must Alan take out from the drawer in a dark room before there is a pair of socks of the same colour?
There are 3 grey socks, 3 blue socks and 3 yellow socks in a drawer. How many socks must Alan take out from the drawer in a dark room before there is a pair of socks of the same colour?
There are 5 blue , 8 green , 9 white and 2 black marbles in the box . At least how many marbles must Darrell draw before he gets the first green one.
a teacher has a bag of sweets for her student. If each student is given 4 sweet, the remaining number of sweet is 4. If each student is given 5 sweet, the given will be short of 20 sweet. how many students are there?