SOLVING PROBLEMS INVOLVING PERMUTATIONS AND COMBINATIONS

In how many ways can you arrange 5 Mathematics books, 4 Science books, and 3 English books on a shelf such that books of the same subject are kept together?

• 17, 280

• 34, 560

• 51, 840

• 103, 680

Answer explanation

In how many ways can 6 students be seated in a row of 6 seats if 2 of the students insist on sitting beside each other?

• 1440

• 240

• 720

• 15

Answer explanation

In a gathering, the host makes sure that each guest shakes hands with everyone else. If there are 25 guests, how many handshakes will be done?

• 300

• 325

• 600

• 650

Answer explanation

Suppose you are the owner of a sari-sari store and you want to put 12 pieces of canned goods in a row on the shelf. If there are 3 identical cans of meat loaf, 4 identical cans of tomato sauce, 2 identical cans of sardines, and 3 identical cans of corned beef, in how many different ways can you display these goods?

• 479,001,600

• 1, 581, 228, 000

• 72

• 277, 200

Answer explanation

A soloist is auditioning for a musical play. If she is required to sing any three of the 7 prepared songs, in how many ways can she make her choice?

• 210

• 35

• 21

• 28

Answer explanation

In a dance contest, each participating group must perform 3 kinds of dance. If there are 4 choices for ballroom dance, 8 choices for foreign dance, and 5 choices for hip-hop, in how many possible ways can a dance group select their piece?

• 17

• 70

• 2,240

• 160

Answer explanation

If 3 marbles are picked randomly from a jar containing 6 red marbles and 8 green marbles, in how many possible ways can it happen that at least 2 of the marbles picked are green

• 224

• 168

• 56

• 288

Answer explanation

There are 10 identified points on a number line. How many possible rays can be drawn using the given points?

• 45

• 90

• 135

• 120

Answer explanation

You are transferring to a new house. You have a collection of books but you cannot take them all with you. In how many ways can you select 7 books out of 10, and then arrange these books on a shelf if there is space enough for only 5 books?

• 2520

• 2,640

• 120

• 302, 400

Answer explanation

At Enzo’s Pizza Parlor, there are seven different toppings, where a customer can order any number of these toppings. If you dine at the said pizza parlor, with how many possible toppings can you actually order your pizza?

• 7

• 5040

• 127

• 135

Answer explanation