The number of ways to arrange the letter of the Words 'BOBLE' and 'VOWELS' Such that all the letters of one word always come together is \( 5!\times 4!\times k(k+1)\left(k^{2}+1\right)\left(\log _{10}\left(k^{3}+2\right)\right) \) find \( k \)

Question

The number of ways to arrange the letter of the Words 'BOBLE' and 'VOWELS' Such that all the letters of one word always come together is \( 5!\times 4!\times k(k+1)\left(k^{2}+1\right)\left(\log _{10}\left(k^{3}+2\right)\right) \) find \( k \)

Answer 1

The arrangements for 'BOBLE':  5!/2!​= 120/2​ =60.

The arrangements for 'VOWELS': 6!=720.

Total arrangements treating each word as a unit: 2×60×720=86400.

Set up the equation: 86400 =5!×4!×k(k+1)(k²+1)(log₁₀​(k³+2)).

Solve for k by substituting values and simplifying the equation.

We get k = 4