Respuesta :
There are 62 number of ways in which classes to these students can be assigned. It can be solved by using the fomula of combination.
What is the formula of combination?
Following is the fomula of combination:
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
Here, n is the total objects available and r is the number of object need to choose from n objects.
Let six friends are A, B, C, D, E, and manoj.
Consider all 6 friends are in chemistry class. Hence, number of ways in which it can be is,
[tex]^6C_6[/tex]
Consider 5 friends are in chemistry class. Hence, number of ways in which it can be is,
[tex]^6C_5[/tex]
Consider 4 friends are in chemistry class. Hence, number of ways in which it can be is,
[tex]^6C_4[/tex]
Consider 3 friends are in chemistry class. Hence, number of ways in which it can be is,
[tex]^6C_3[/tex]
Consider 2 friends are in chemistry class. Hence, number of ways in which it can be is,
[tex]^6C_2[/tex]
Consider 1 friend is in chemistry class. Hence, number of ways in which it can be is,
[tex]^6C_1[/tex]
Consider no friend is in chemistry class all are in biology class. Hence, number of ways in which it can be is,
[tex]^6C_0[/tex]
Hence, total number of ways in which classes can be assigned to 6 students is,
[tex]^6C_6+^6C_5+^6C_4+^6C_3+^6C_2+^6C_1+^6C_0=64[/tex]
Now, the number of ways in which mnoj is alon. There are two ways. Either he will be in the chemistry class or he will be in the physics class.
Hence, subtract 2 from 64 to get the answer.
[tex]64-2=62[/tex]
Hence, there are 62 number of ways in which classes to these students can be assigned.
Learn more about combination from the following link:
https://brainly.com/question/11732255
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