Counting problems for Grade 4

7 problems with worked solutions.

№ 1 · Counting · Grade 4

A grid has five rows and seven columns of cells. How many rectangles can be outlined along its grid lines?

№ 2 · Counting · Grade 4

Five participants greeted one another, with each pair greeting exactly once. How many greetings were there?

№ 3 · Counting · Grade 4

One hundred lockers are numbered in order. Every fourth locker is marked red, and every sixth locker is marked blue. How many lockers have at least one mark?

№ 4 · Counting · Grade 4

A robot moves on a square grid from the lower-left corner to the upper-right corner. It must take exactly 3 steps right and 2 steps up. How many shortest routes are possible?

№ 5 · Counting · Grade 4

How many three-digit numbers can be made from the digits 1, 2 and 3 if each digit must be used exactly once?

№ 6 · Counting · Grade 4

Choose 2 books from 6 different books for a trip. How many choices are possible if order does not matter?

№ 7 · Counting · Grade 4

Three-digit numbers are made from the digits 1, 2, and 3, using each digit exactly once. How many such numbers are possible?