Erasmus+ Project- Hooked on Mathematics

1. Variations

2. Variations without a repetition of the k-class n element (k <n) are
called such compounds, each of which contains different elements
of given n and differ from one another or the elements or the
order of the elements.
𝑉𝑛
𝑘 =
𝑛!
𝑛 − 𝑘 !
= 𝑛. 𝑛 − 1 𝑛 − 2 … … 𝑛 − 𝑘 + 1

3. Example 1: 8 athletes participate in the swimming contest at the
World Athletics Championship. In how many different ways can be
the gold, silver and bronze medals distributed if it is known that
the Bulgarian representative will surely take the gold medal?
𝑉7
2
= 7.6 = 42

4. Example 2: How many two-digit numbers with different digits can
be written with the digits 1, 2, 3 and 4?
𝑉4
2
= 4.3 = 12

5. Example 3: How many 3-note music chords can we form from 6
different notes?
𝑉6
3
= 6.5.4 = 120

6. Example 4: А phone number consists of 7 different digits. How
many options are available for the remaining 5 digits if the
number starts with 97?
97_ _ _ _ _
10-2=8
𝑉8
5
= 8.7.6.5.4 = 6720

7. Example 5: Only 3 or 4 letters are used in the language of the
AOEIU tribe. These letters are A, O, E, I and Y. How many words
does the complete dictionary of the words from the language of
the tribe consist of ?
𝑉5
3
+ 𝑉5
4
= 5.4.3 + 5.4.3.2 = 60 + 120 = 180