Can you pls help me on these items? Pls pls. Thank you so much.

Subject: Pre-Algebra- Probability and Statistics

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Activity 1:

Answer each given situation below. Show complete computations, then box all final answers. 1. There are 12 athletes joining the Baguio Marathon Event. How many ways can the first, second, and third placers be chosen? 2. Five boys and four girls are to arrange themselves to form a line. How many arrangements can there be if: (a) the boys stand together, and the girls stand together? (b) the boys and the girls stand alternately? 3. There are 10 participants to a barangay meeting to talk about safety measures to be implemented during the pandemic. In how many ways can these 10 barangay participants arrange themselves in a row if three of them should stay together? 4. A couple with their three children are to pose for a family picture. In how ways can they be arranged in a row if: (a) they can take any position? (b) the mother and the father stay at both ends? (c) In how many ways can they be arranged in two rows if the parents will stay at the front row?DIRECTIONS: Read and analyze each item carefully. Write the letter of the correct answer on the blank provided for. 1. If one event can occur in m ways and a second thing can occur in n ways, then which expression gives the number of ways both events can occur? A) m! n! B)m x n C) m! DJ n! 2. Which expression is equivalent to n!? A) n(n - 1)(n - 2)...2x 1 C) n(n - 1) B)n- (n - 1) D) (n - 1) (n - 2) 3. It is referred to as an arrangement of things in definite order or distinct arrangement of distinguishable objects. A) factorial B) tree diagram C) permutation D) listing 4. A coat hanger has four knobs, and each knob is to be painted by a distinct color. If six different colors of paint are available, how many ways can the knobs be painted? A) 24 B) 360 C) 720 D) 1,296 5. Evaluate 7P5. A) 42 B) 120 C) 2,520 D) 5,040 6. A new model of a car is available in six exterior colors, three interior colors, and two interior styles. How many versions of car are available for order? A) 2 B) 6 C) 36 D) 720 7. A multiple-choice test contains five questions, and each question has four options. In how many ways can the five questions be answered? D) 1,024 A) 20 B) 25 C) 6258. A bookshelf has five different Algebra books and n different Geometry books. If there are 40,320 ways to arrange the books on the shelf, how many Geometry books are on the bookshelf? A) 6 B) 5 C ) 4 D) 3 9. How many ways can the letters from the word FLEA be arranged such that each "word" starts with a consonant and ends with a vowel? A) 8 B) 12 C) 24 D) 27 Use this situation for items 10 to 14. How many three-digit numbers can be formed using the digits 5, 7, 8 and 2 if: 10. the digits cannot be repeated? A) 24 B) 64 C) 256 D) 512 1 1. repetition of digits is not allowed, and the number is less than 700? A) 48 B) 24 C) 12 D) 6 12. 5 is the first digit and repetition is not allowed? A) 6 B) 8 C) 10 D) 12 13. 5 is the first digit, 2 is the second digit, and repetition of digits is allowed? A) 6 B) 8 C) 4 D) 2 14. 5 is the first digit, 2 is the last digit, and repetition of digits is not allowed? A) 16 B) 8 C) 4 D) 2 15. How many permutations are there in the letters of the word HELPING if ING remain in that order? A) 1,000 B) 720 C) 380 D) 120