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🎯 Final Answer: The ratio of the total surface areas of the smaller cubes to the large cube is 25:18. 🎊

🎯 Final Answer: The total number of ways to form the committee is 756! 🎊

🎯 Final Answer: The total number of ways the letters of LEADING can be arranged such that the vowels always come together is 720! 🎊

Remember: Group the vowels together as a single "block" or unit.(Treat the vowels as one entity so they always stick together.) Count the remaining units:The number of units to arrange = Total...

Remember : We need to select 3 consonants from the 7 available consonants. The number of ways to do this is given by the combination formula (nr)\binom{n}{r}(rn​), where n is the total number and r is...

Quick trick! 🎉 The word LEADER has 6 letters, with E repeating twice. The number of arrangements is 6!2!=360\frac{6!}{2!} = 360. 🎉

Quick trick! 🎉 Total ways to select 4 children from 10 (6 boys, 4 girls): (104)=210\binom{10}{4} = 210 Ways to select 4 girls (no boys): (44)=1\binom{4}{4} = 1 Subtract the no-boy case from the...

We need to form 3-digit numbers using the digits 2, 3, 5, 6, 7, 9 ✅ Divisible by 5 ✅ No repeated digits Step 1: Check divisibility by 5 🔢 For a number to be divisible by 5, its last digit must...

Quick Trick: Calculate combinations for men: C(8,5)=56C(8, 5) = 56. Calculate combinations for women: C(10,6)=210C(10, 6) = 210. Multiply the results: 56×210=1176056 \times 210 = 11760. So,...

Let's solve this step by step in a simple and fun way! 🎉 Step 1: Identify the given balls ⚪⚫🔴 The box contains: 2 White balls ⚪⚪ 3 Black balls ⚫⚫⚫ 4 Red balls 🔴🔴🔴🔴...

Let's solve this step by step in a simple way! 🎉 We need to arrange the letters of DETAIL so that vowels (E, A, I) only occupy the odd positions. ✅ Step 1: Identify vowels and consonants 🔤...

We need to form a group of 5 men and 2 women from: 7 men 👨👨👨👨👨👨👨 3 women 👩👩👩 Step 1: Choose 5 men from 7 👨‍💼 We select 5 men from 7. The number of ways to...

Step 1: Identify the given people 👨‍💼👩‍💼 We have: 7 men 👨👨👨👨👨👨👨 3 women 👩👩👩 We need to form a group of 5 men and 2 women. ✅ Step 2: Choose 5 men...

Step 1: Count the total distinct letters The word LOGARITHMS has 10 distinct letters:L, O, G, A, R, I, T, H, M, S (no repetitions). Step 2: Select 4 letters Since we need to form a 4-letter word, we first...

Step 1: Identify the vowels and consonants ✨ The word MATHEMATICS has 11 letters 🅰️🔤 Vowels (🟢): A, E, A, I Consonants (🔵): M, T, H, M, T, C, S Step 2: Treat the vowels as one unit...

The word OPTICAL consists of 7 distinct letters:O, P, T, I, C, A, LIt contains 3 vowels: O, I, A and 4 consonants: P, T, C, L. Step 1: Treating the vowels as a single unit Since the vowels O, I, A must...