 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that find the number of ways in which our garland of 10 roses are formed such that each rose is of different color. We know that the number of ways in which n different things can form a ring is given by n minus 1 factorial. That is if we have to make circular arrangement for n number of objects then we fix the position of one object and the remaining n minus 1 number of objects can be arranged in n minus 1 factorial number of ways or we can say the number of ways in which n different things can form a ring is given by n minus 1 factorial. Also we know that number of circular arrangements of n different things when clockwise and anti-clockwise arrangements are not different is given by 1 by 2 into n minus 1 factorial that is the number of circular arrangements of n different things when clockwise and anti-clockwise arrangements are different is given by 1 by 2 into n minus 1 factorial. With this key idea let us proceed with the solution. Now according to the question we need to find the number of ways in which a garland can be formed with 10 roses such that each rose is of different color. We know that there are 10 roses to form a garland that is 10 roses are to be placed in a circular manner and we know that the number of ways in which n different things can form a ring is given by n minus 1 factorial that is if we have n number of objects we fix the position of one object and the remaining n minus 1 objects can be arranged in n minus 1 factorial number of ways. So on fixing the position of one rose the remaining 9 roses can be arranged in 10 minus 1 factorial number of ways that is 9 factorial number of ways as there is no distinction between the clockwise anti-clockwise arrangements and we know that the number of circular arrangements of n different things when clockwise and anti-clockwise arrangements are not different is given by 1 by 2 into n minus 1 factorial therefore the required number of ways are given by 1 by 2 into 10 minus 1 factorial which is equal to 1 by 2 into 9 factorial. Hence the number of ways in which 10 roses each of different color can be arranged is given by 1 by 2 into 9 factorial which is our final answer. This completes our session. Hope you enjoyed this session.