There are six periods in each working day of a school. Number of ways in which 5 subjects can be arranged if each subject is allotted at least one period and no period remains vacant is

Question

There are six periods in each working day of a school. Number of ways in which 5 subjects can be arranged if each subject is allotted at least one period and no period remains vacant is (A) 210 (B) 1800 (C) 360 (D) 120

Tardigrade Admin · Accepted Answer

Atleast one period is repeated, which can be selected in 5 C1 ways. Now 6 subjects can be arranged in (6 !/2 !) ways. Hence total number of ways are 5 × (6 !/2 !)=1800

Q. There are six periods in each working day of a school. Number of ways in which $5$ subjects can be arranged if each subject is allotted at least one period and no period remains vacant is

210

1800

360

120

Atleast one period is repeated, which can be selected in $^{5} C_{1}$ ways.
Now $6$ subjects can be arranged in $\frac{6 !}{2 !}$ ways.
Hence total number of ways are $5 \times \frac{6 !}{2 !} = 1800$

Q. There are six periods in each working day of a school. Number of ways in which 5 subjects can be arranged if each subject is allotted at least one period and no period remains vacant is

210

1800

360

120

Atleast one period is repeated, which can be selected in 5C1​ ways. Now 6 subjects can be arranged in 2!6!​ ways. Hence total number of ways are 5×2!6!​=1800

Q. There are six periods in each working day of a school. Number of ways in which $5$ subjects can be arranged if each subject is allotted at least one period and no period remains vacant is

Atleast one period is repeated, which can be selected in $^{5} C_{1}$ ways.
Now $6$ subjects can be arranged in $\frac{6 !}{2 !}$ ways.
Hence total number of ways are $5 \times \frac{6 !}{2 !} = 1800$