**(1). Evaluate 5P3**

**(a). 60 (b). 30 (c). 20**

**Solution Using Casio fx991es**

**[ON] [5] [SHIFT] [nPr] [3] [=]**

**Therefore Option A is correct.**

**(2). Evaluate 5P3 + 6P2**

**(a). 90 (b). 40 (c). 20**

**Solution Use Casio fx991es**

**[ON] [5] [SHIFT] [nPr] [3] [+] [6] [SHIFT] [nPr] [2] [=]**

**Therefore Option A is correct.**

**(3). If nP2 = 30 find n**

**(a). 6 (b). 3 (c). 2**

**In this case you pick any number from the option and if it gives exactly the same number at the right axis that is after = sign then it is correct.**

**Checking Option A**

**Solution Using Casio fx991es**

**[6] [SHIFT] [nPr] [2] [=]**

**Therefore Option A is correct because it gives 30 as the answer.**

**(4). Find the value of n if p (n, 2) = 72**

**(a). 9 (b). 3 (c). 6**

**It is also in these form nPr but r has been given as 2 and you are meant to find the value of n**

**You pick any number from the option and make it to be n and if it gives the same answer at the right axis that is after the = sign then the option is correct.**

**Checking Option A**

**Solution Using Casio fx991es**

**[ON] [9] [SHIFT] [nPr] [2] [=]**

**Therefore Option A is correct.**

**(5). If 9Pr = 72 find the value of r**

**(a). 2 (b). 3 (c). 5**

**It is also in these form nPr but n has been given as 9 and you are meant to find the value of r, therefore pick any number from the option and make it to be r and if it gives the same answer at the right axis that is after the = sign then the option is correct.**

**Checking Option A**

**Solution Using Casio fx991es**

**[ON] [9] [SHIFT] [nPr] [2] [=]**

**Therefore Option A is correct.**

**(6). If X! = 24 find X**

**(a). 4 (b). 2 (c). 1**

**Choose from the option and make it to be the unknown value X and if it gives the same answer at the right axis that is after the = sign then the option is correct.**

**Checking Option A**

**Solution Using Casio fx991es**

**[ON] [4] [SHIFT] [x!] [=]**

**Therefore Option A is correct.**

**(7). If nP7 = 6 nP6 then find n**

**(a). 12 (b). 6 (c). 3**

**In this case you pick any number from the option and make it to be n and if the answer at the left axis before the = sign is equal to the right axis that is after the = sign then the option is correct.**

**Checking Option A**

**Solution Using Casio fx991es**

**[ON] [1] [2] [SHIFT] [nPr] [7] [=]**

**It gives 3991680 and if the right axis gives the same answer then the option is correct.**

**Solution Using Casio fx991es**

**[ON] [6] [×] (multiplication sign) [1] [2] [SHIFT] [nPr] [6] [=]**

**It also gives 3991680 as the answer at the right axis, Therefore Option A is correct.**

**(8). In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women**

**(a). 63 (b). 64 (c). 126**

**In this case you either pick the highest number of men or women. (Ie. You pick the highest number of men which is 7 and then combinate it with the lowest number of men which is 5 then multiply it by the highest number of women which is 3 and then combinate it with the lowest number of women which is 2)**

**Example in 7C5 × 3C2**

**Solution Using Casio fx991es**

**[ON] [7] [SHIFT] [nCr] [5] [×] (multiplication sign) [3] [SHIFT] [nCr] [2] [=]**

**Therefore Option A is correct because it gives answer as 63**

**(9). How many 3 digits numbers can be formed using the digits 1, 2, 3, 4, 5 if no repetition is allowed.**

**(a). 60 (b). 30 (c). 10**

**In this case you choose the the one that has the highest digit number eg in these digits 1, 2, 3, 4, 5 it has a total of 5 digit therefore it is higher than 3 digit from the question sometimes in some cases 3 digits from the question can be higher eg. It might be 7, therefore pick the highest digit number which is 5 we get by the total number of digits given to us or the cardinality of the digits numbers given to us and then permutate it with the lowest number of digits given that is 3, It works when 0 is not in the digits given or in the cardinality of the digits.**

**Example in 5P3**

**Solution Using Casio fx991es**

**[ON] [5] [SHIFT] [nPr] [3] [=]**

**Therefore Option A is correct.**

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