INIT #2 COUNTING METHODS TEST PART I]: Show all of your work to support your solutions, including formulas used and explanations when necessary for full marks. APPLICATION 1. WHAT IS THE NUMBER OF PERMUTATIONS OF THE WORD EXPONENT IF THE VOWELS MUST ALL BE TOGETHER? 2. ILLUSTRATE YOUR SOLUTION TO THE FOLLOWING PROBLEM USING A TREE DIAGRAM. HOW MANY DIFFERENT HOCKEY UNIFORMS ARE POSSIBLE IF THERE ARE THREE JERSEYS, TWO PANTS AND THREE TYPES OF SOCKS TO CHOOSE FROM? 3. WHICH ROW NUMBER IN PASCAL'S TRIANGLE HAS A SUM OF 256? SHOW YOUR WORK USING A FORMULA. 4. AT A TRACK MEET, FOUR ENTRANTS OF EQUAL ABILITY ARE COMPETING. WHAT IS THE PROBABILITY (AS A DECIMAL ROUNDED TO 4 DP] THAT THE FINISH WILL BE IN THE ORDER OF THE ENTRANTS' AGES {EITHER ASCENDING OR DESCENDING ORDER}? 5. HOW MANY 5 CARD POKER HANDS CAN BE MADE WITH 2 ACES AND 3 QUEENS FROM A STANDARD DECK OF 52