Problem 6 * [10 pts]: Free Sharky You and secret agent Raj(he/h1m) have found a Blahaj (shown in Figure) caged by the dreaded Dr. Complexity(she/her). This cage is locked by a digital lock labelled 510510. This lock needs 4 different digital keys to open. Each key contains a different factor of 510510 such that the product of all 4 numbers is 510510. Furthermore, none of the keys have the number 1 stored. When all 4 loeys are inserted, the lock's software will check for these numbers. If all 4 unique numbers are detected, the lock opens. Raj also informs you 510,510 is the product of 7 primes: 510510=23571113t17 So example keys can looks like the following, each example a unique variation: 0 Key 1 has the number 6. Key 2 has the [W 35. Key 3 has the number 143. Key 4 has the number 17. 0 Key 1 has the number 35. Key 2 has the number 143, Key 3 has the number 6. Key 4 has the number 17. 0 Key 1 has the number 30. Key 2 has the number 13. Key 3 has the number 17. Key 4 has the number 77. Raj state; there are 8,400 possible combinations of 4 keys to try. Show that Raj's statement about the number of possible combinations is correct. (Hint: List all the possible ways you can make a set of 4 keys rst. Then consider how the order of the keys affects your answer.) Epilogue: You create the correct 4 keys on the rst try. With the Blahaj freed, Dr. Complexity surrenders. As shown in Figure I], they are happy to be free