26 Represent the following data in ungrouped frequency table which gives the number of chiddren in 25 familles. \( 1,3,0,2,5,2,3,4,1,0,5,4,3,1,3,2,5,2,1,1,2,6,2,1,4 \) 27 . If you have 2 school bags and 3 water bottles then, in how many different ways can you choose each one of them, while going to school? 28. Using repeated division method, find the HCF : 455 and 26 .

Sure, let's tackle each problem one by one. --- ### **Problem 26** **Represent the given data in an ungrouped frequency table:** **Data Set:** \( 1, 3, 0, 2, 5, 2, 3, 4, 1, 0, 5, 4, 3, 1, 3, 2, 5, 2, 1, 1, 2, 6, 2, 1, 4 \) **Steps to Create the Frequency Table:** 1. **Identify the Distinct Values:** The number of children can be 0, 1, 2, 3, 4, 5, or 6. 2. **Count the Frequency of Each Value:** - **0:** Appears **2** times - **1:** Appears **6** times - **2:** Appears **6** times - **3:** Appears **4** times - **4:** Appears **3** times - **5:** Appears **3** times - **6:** Appears **1** time 3. **Create the Table:** | Number of Children | Frequency | |--------------------|-----------| | 0 | 2 | | 1 | 6 | | 2 | 6 | | 3 | 4 | | 4 | 3 | | 5 | 3 | | 6 | 1 | --- ### **Problem 27** **Determine the number of different ways to choose one school bag and one water bottle.** - **Number of School Bags:** 2 - **Number of Water Bottles:** 3 **Calculation:** For each choice of a school bag, there are 3 choices of water bottles. \[ \text{Total Ways} = \text{Number of School Bags} \times \text{Number of Water Bottles} = 2 \times 3 = 6 \] **Answer:** There are **6 different ways** to choose one school bag and one water bottle. --- ### **Problem 28** **Find the HCF (Highest Common Factor) of 455 and 26 using the Repeated Division (Euclidean) Method.** **Steps:** 1. **Divide 455 by 26:** \[ 455 \div 26 = 17 \text{ with a remainder of } 13 \] So, \[ 455 = 26 \times 17 + 13 \] 2. **Now, divide 26 by the remainder 13:** \[ 26 \div 13 = 2 \text{ with a remainder of } 0 \] Since the remainder is now 0, the divisor at this step (which is 13) is the HCF. **Answer:** The HCF of 455 and 26 is **13**. --- Feel free to ask if you have any more questions!