There are 8 students appearing in an examination of which 3 have to appear in Mathematics paper and the remaining 5 in different subjects. Then, the number of ways they can be made to sit in a row, if the candidates in Mathematics cannot sit next to each other is:
Explanation
Calculation:
Given: 8 students appearing in an examination of which 3 have to appear in Mathematics paper and the remaining 5 in different subjects.
There are 5 candidates not appearing in mathematics.
Let us arrange these 5 in a row, each shown by X.
They can be arranged in 5!=120 ways.
On both sides of each X, we put an M, as shown below:
Now, 3 candidates in mathematics can be arranged at 6 places in 6P3 ways:
6P3=(6−3)!6!=6×5×4=120 ways
Hence, the total number of arrangements:
Explanation
Calculation:
Given: 8 students appearing in an examination of which 3 have to appear in Mathematics paper and the remaining 5 in different subjects.
There are 5 candidates not appearing in mathematics.
Let us arrange these 5 in a row, each shown by X.
They can be arranged in 5!=120 ways.
On both sides of each X, we put an M, as shown below:
Now, 3 candidates in mathematics can be arranged at 6 places in 6P3 ways:
6P3=(6−3)!6!=6×5×4=120 ways
Hence, the total number of arrangements:
