The Partial Permutations of N items taken K at a time is:
N! / (N - K)!
For N = 9 and K = 3, we get
9! / 6! = 7*8*9 = 504 possible three digit numbers.
Of those, odd are those which end in 1,3,5,7,9 (5 accepted endings) from a total of 1,2,3,4,5,6,7,8,9 (9 possible endings).
So, we take 5/9 of 504.
(5/9)*504 = 280.
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 ~
Câu 1: How many distinct 3 - digit odd numbers can you make by using 0;1;2;4 and 5 ? (Giải thích rõ giúp mình)
Câu 2: How many distinct 4 - digit numbers are divisible by 2 can be form from digits 0;2;5;6 and 9 ? (Giải thích rõ luôn nha)
Câu 10:How many 3-digit odd numbers can you make by using 3, 2, 5, 4 and 6?Answer: There are numbers
How many 3-digit odd numbers can you make by using 3, 2, 5, 4 and 6?
Answer: There are
numbers
Use all the digits below to form the decimal number that is smaller than 5.
2; 5; 9; 4; 8
How many such numbers are there?
Use all the digits below to form the decimal number that is smaller than 5
2, 5, 9, 4, 8
How many such numbers are there?
Answer: numbers.
giúp mình nha! mình tick cho 5 cái
Use all the digits below to form the decimal number that is smaller than 5.
2; 5; 9; 4; 8
How many such numbers are there?
Question 6:
Use all the digits below to form the decimal number that is smaller than 1
How many such numbers are there?
Answer: numbers.
