Combination of r Things from n Things When All Are Not Different

Q. Number of ways of selecting 6 shoes, out of 8 pairs of shoes, having exactly two pairs is

1. 1680
2. 240
3. 120
4. 3360

Q. In a shop there are five types of ice creams available. A child buys six ice creams.
Statement 1: The number of different ways the child can buy the six ice-creams is
${}^{10}{C}_5$.
Statement 2: The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A's and 4 B's in a row.

1. Statement 1 is false, statement 2 is true.
2. Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1.
3. Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1.
4. Statement 1 is true, statement 2 is false.

Q. What is the value of the subtraction of $5$ from $4$ ?

Q.

Let $A=\{lettersofNEWJERSEY\}$and $B=\{lettersofNEWYORK\}$

Find $B\cap A$