there is a long table having 8 chairs on each side .there are 16 persons who are to be seated for a tea party.4 of them want to sit on a particular side and 2 other want to sit on the other side. in how many ways all the 16 people may be seated for the tea party
To find the number of ways all the 16 people may be seated for the tea party, we need to consider the arrangement of people on each side of the table separately.
First, let's consider the side where 4 people want to sit. We have 8 chairs on each side, and we need to choose 4 out of the 8 chairs on this side for the 4 people. This can be done in C(8,4) ways, which is the combination formula and evaluates to 70 ways.
Next, let's consider the side where 2 other people want to sit. Similarly, we have 8 chairs on this side, and we need to choose 2 out of the 8 chairs for the 2 people. Again, this can be done in C(8,2) ways, which is also equal to 28 ways.
Now, since these two sides are independent of each other, we can multiply the number of ways for each side to get the total number of arrangements:
Total number of arrangements = 70 ways (for the first side) * 28 ways (for the second side)
Therefore, the total number of ways all the 16 people may be seated for the tea party is 70 * 28 = 1960 ways.