Question

Six distinct integers are picked from the set {1, 2, 3,…, 10}. How many selections are there, in which the second smallest integer in the group is 3?

Answer 1

Answer:

1680 ways

Step-by-step explanation:

Total number of integers = 10

Number of integers to be selected = 6

Second smallest integer must be 3. This means the smallest integer can be either 1 or 2. So, there are 2 ways to select the smallest integer and only 1 way to select the second smallest integer.

2 ways   1 way                                      

Each of the line represent the digit in the integer.

After selecting the two digits, we have 4 places which can be filled by 7 integers. Number of ways to select 4 digits from 7 will be 7P4 = 840

Therefore, the total number of ways to form 6 distinct integers according to the given criteria will be = 1 x 2 x 840 = 1680 ways

Therefore, there are 1680 ways to pick six distinct integers.