The Number of ways of arranging 3 out of 7 painting is, 35.
The Number of ways of his look to the painting is 84
Permutation and combination :
It is given that,
A museum has 7 paintings by Picasso and wants to arrange 3 of them on the same wall.
We have to select 3 out of 7 and arrange it.
Number of ways of arranging 3 out of 7 painting is,
[tex]=^{7}C_{3}\\ \\=\frac{7!}{3!*4!} =\frac{7*6*5*4!}{3*2*4!}=35[/tex]
When 9 people come to view the 3 paintings,
Number of ways of his look to the painting is ,
[tex]=^{9}C_{3}\\ \\=\frac{9!}{3!*6!}=\frac{9*8*7*6!}{6*6!}=84[/tex]
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