the following and show your solution Topic: combinatorics 1. 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? 2. 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? 3. In a gathering, the host makes sure that each quest shakes hands with everyone else. If there are 25 guests, how many handshakes will be done? * 4. 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? 5. 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 6. In a dance contest, each participating group must perform 3 kinds of dance. If there are 4 choices for ballroom dance, & choices for foreign dance, and 5 choices for hip-hop, in how many possible ways can a dance group select their piece? 7. 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