Answer:
1560780 selections
Step-by-step explanation:
Given
Cars = 29
Selection = 7
Required
Possible number of selections
The interpretation of the question is that, in how many ways can 7 cars be selected from 29.
This is done using combination formula as follows:.
[tex]^nC_r = \frac{n}{(n-r)!r!}[/tex]
Where
[tex]n = 29[/tex]
[tex]r = 7[/tex]
So, the formula becomes:
[tex]^{29}C_7 = \frac{29!}{(29-7)!7!}[/tex]
[tex]^{29}C_7 = \frac{29!}{22!7!}[/tex]
[tex]^{29}C_7 = \frac{29*28*27*26*25*24*23*22!}{22!7!}[/tex]
[tex]^{29}C_7 = \frac{29*28*27*26*25*24*23}{7!}[/tex]
[tex]^{29}C_7 = \frac{29*28*27*26*25*24*23}{7*6*5*4*3*2*1}[/tex]
[tex]^{29}C_7 = \frac{7866331200}{5040}[/tex]
[tex]^{29}C_7 = 1560780[/tex]
Hence, the number of ways is 1560780
