nCr and nPr 4 (5m)

Can you please help me? Thank you. 5 marks

Please show steps.
1. Kitty wants to choose 3 out of 13 different items as the Christmas presents. Given that 4 items are from shop A, 6 items are from shop B and 3 items are from shop C, find the number of combinations if choosing at least 1 item from shop A.

Solutions for Q1 - 202

2. There are 50 buttons on a calculator. 5 of them do not work. If 4 different buttons are selected, find the number of combinations if
(a) only one button selected does not work.
(b) at least one button selected does not work.

Solutions Q2 - (a) 70 950
(b) 81 305

3. It is given that the product of 5 prime numbers 11, 13, 17, 19 and 97 is 4 480 333. How many positive factors of 4 480 333 are there?
Hint: Are 11 x 13, 13 x 17, 11 x 17 factors of 4 480 333? Is 11 x 13 x 17 a factor of 4 480 333?

Solutions Q3 - 32